The answer to this question can't be found directly in the RAW, so we must engage in some speculation, specifically the success of the action hinges on what you see when you look into a Bag of Holding and what you see when you look out of it. Let's look at the descriptions:
Misty Step:
Briefly surrounded by silvery mist, you teleport up to 30 feet to an unoccupied space that you can see. (PHB pg. 260)
Bag of Holding:
This bag has an interior space considerably larger than its outside dimensions, roughly 2 feet in diameter at the mouth and 4 feet deep. The bag can hold up to 500 pounds, not exceeding a volume of 64 cubic feet. The bag weighs 15 pounds, regardless of its contents.... Breathing creatures inside the bag can survive up to a number of minutes equal to 10 divided by the number of creatures (minimum 1 minute), after which time they begin to suffocate... (DMG pgs. 153-154).
As you can see there are several requirements that must be met for you to able to accomplish this action:
You must not put the weight of the items inside the bag to over 500 lbs, meaning that you must add your character weight, items you are carrying, and items already inside the bag to see if you exceed the weight limit (if you do the bag breaks and its contents are set adrift in the astral plane!).
You must not stay in the bag for more that 10 minutes (assuming your the only one in there) lest you suffocate.
As per Misty Step you must be able to see where you are going- which is where the speculation begins.
Since you have to see where you are going, you will not be able to teleport into or out of a closed bag, but if the bag is open and you can look inside you might be able to justify the this action (similarly, if you can see out of the bag when inside). So basically what it comes down to is the description of what you see when you look inside (or outside) the bag. Since no official source (to my knowledge) contains such a description it would be the DM's call. If you can see a tiny storage room with all your items or even a sea of floating items you could probably justify using misty step, but if you see blackness, a void, or even just an empty bag you can't use Misty Step.
In conclusion - Maybe, it depends on whether or not you can see into or out of the open bag's item storage area (I'm hesitant to say that it is an extradimensional space b/c it is not specifically stated in the RAW) which is dependent on how your DM describes the bag. However, even if your DM excepts this justification, it may be much easier for you (depending on your size) just jump in normally.
Officially, ask the GM
There's no official answers to these questions beyond a couple of sidelong mentions, so the DM must answer them if they come up, like, for example, if the party expects to be spending a large amount of time within their bag of holding (maybe by using a bottle of air or a necklace of adaptation).
Unofficially, here's some speculation
I've speculated below about some things and drawn some conclusions based on the limited information presented by the text about others, but none of these are official, and I'm unaware of an official stance on any of the questions raised.
Stocking the bag
The first problem of shoving a refrigerator-sized box into a bag of holding is, frankly, shoving the refrigerator-sized box into it. The bag is only 2 ft. wide and, unless the GM says the bag does, that opening doesn't stretch to accommodate stuff. So while that opening could accommodate a human child...
...or a Medium adult, a standard-size kitchen-type refrigerator box would likely be too big.
Gazing into the bag
But let's say that one does get whatever into one's bag of holding then sets down the bag and takes a look inside. What does one see?
A bag of holding opens into an extradimensional space in its own demiplane... usually.1 Whether that demiplane is naturally illuminated or not is up to the DM.
- If a bag's interior is naturally illuminated, can an open bag be used for illuminating an area when one's out of torches? Can one enter the bag, read by such light, and exit the bag if one doesn't exceed the weight limit or overstay the breathable air time limit?
- If the bag's interior is not illuminated does one take longer than a full-round action to extract an item from an overloaded bag, contrary to the bag's description, because of one's inability to see the bag's contents?
Reaching into the bag
Assuming one can always fish items from an unoverloaded2 bag as a move action or from an overloaded bag as a full-round action, the magic of the bag must keep its contents sort of organized, respond to the possessor's will, some DM-determined combination of both, or something entirely different. That's because the bag must be more organized and convenient than a backpack: while the move action retrieve an item provokes attacks of opportunity,
Retrieving a specific item from a bag of holding is a move action, unless the bag contains more than an ordinary backpack would hold, in which case retrieving a specific item is a full-round action.
So while just as much—if not more—effort is needed to retrieve an item from a bag of holding, technically doing so while threatened is not as dangerously distracting as retrieving an item from, for example, a backpack.
Thus the DM has at least two choices:
- The possessor of the bag looks into the bag and sees all the contents as if through a telescope, and is able to manipulate the bag opening to see into different parts of the bag. If the bag's overloaded, one searches the bag with quick glances while keeping an eye on one's foe, I guess.
- The possessor of the bag sees an empty bag (or, alternatively, what would be the contents of a normal bag of that size) but can mentally manipulate (perhaps sliding like a touchscreen) objects within the bag until the correct one comes into view. This manipulation is rapid but not distracting, so one can keep one's eye on one's foe.
Stacking stuff in the bag
Whether stacked items fall over in the bag is the DM's call. For the first kind of bag described above, I'd argue No, the items remain stacked. That demiplane is stable. However, one must be careful when putting new things into such a bag so that they don't crush sensitive items already inside. For the second kind of bag, I'd argue Yes, the stacked items fall. The second case uses a multiple but limited number of what are, essentially, sub-bags within the main bag (that number being up to the DM, but likely each as big as a regular bag or, I dunno, like, infinite, each one capable of holding a sling or a piece of chalk).
Personal experience
The handful of times this has come up, I've used the stable bag model, depositing bag-stored items on the translucent, illuminated, spongy, gray surface of the bag's own exclusive demiplane. I've never told the PCs that a dense item carelessly tossed into a bag (which is, usually, instead, a handy haversack) crushed a fragile item because I figure that when an adventurer tosses treasure into his bag, he's careful not to crush other treasure while doing so. Some DMs might not be so kind. But, then again, I've also never had PCs stack a series of items on top of one another in an effort to shortcut the expected time to to extract a lone item from the bag. That might change my mind (or, at least, see their foes start doing the same).
1 The Knights of the Dinner Table comic book illustrates plots that may develop in a campaign wherein bags of holding share a demiplane in The Bag Wars Saga.
2 Not a real word.
Best Answer
You can try, and perhaps succeed (easier with two PCs)
You have the set up for a great idea for dispatching a human sized foe. Or maybe, you want to give them a vacation on the astral plane and they aren't very keen on the idea.
Shoving (work a little with your DM on this part)
Strictly speaking, the rules are silent on a targeted shove, but there's no reason that you can't try to target a shove. Shove and/or grapple is an ability check; it will be an opposed ability check per Chapter 7 and/or Chapter 9.
Your PC can move them once you grapple them, but it's still tricky to stuff them into that hole; I think calling for a shove is a good application of that rule, or, the DM could call for a general Strength check per Chapter 7.
What else you need: two ten foot poles, tied together.
Or two spears, two lances, something that is more than 10' long. Let's say that we want 14' of reach to stay outside of the 10' blast radius of the astral plane entry event.
Aside: if two members of your party can cast Mage Hand, one mage hand can be used to hold the empty bag open while the other mage hand can put the full bag into the empty bag, and keep all of you outside the 10' danger radius.
This ability check may be made with disadvantage
Or not. That's up to your DM.
And here's how it works.
a. You can hold the bag of holding, make a Grapple (and then if you succeed) make a Shove attempt. You are trying to shove them into the bag; since shoving isn't necessarily targeted, you may get disadvantage on this attempt.
Were I DM, I might lay disadvantage on this attempt, and I might not. If the target were a gnome, I'd not lay on disadvantage. You can also apply the 'Shove Aside' optional rule (DMG, p. 252). This lets you make a shove attack to move a creature in an arbitrary direction, but you do so with disadvantage. (thanks to @BBeast for suggesting a reference to that).
With two successes in a row, into the bag they go. If you do not have additional attacks, for example a rogue or an artificer, then it takes two turns to do this and there may be an additional chance to fail as the grappled creature tries to escape the grapple.
We are pretty sure that the bag of holding can't be opened from the inside
b. Open the second (empty) bag of holding, and then carefully drape the (full) bag containing the bagged creature over the end of the pole mentioned above. Make sure you are more than 10' away from the empty bag. Carefully lift the pole and place the full bag into the empty bag.
The bag of holding is indeed "a similar item." They just got a one way ticket to the astral plane.
a. Make sure that your ally uses the help action to assist you with the shove into the bag. That gives you advantage. This will either cancel the disadvantage the DM gave you, above, or it will make for a more likely success.
b. Proceed as above with the poles, and have the ally help you again. The DM may require an ability check to get the full bag into the empty bag, so having advantage on that check is a good plan.
Set yourself up for success!
Get the party's Bard to lay some bardic inspiration on you.
Get the Cleric or the Druid to cast guidance on your character; additions to the ability check are handy here!
If there is a spell caster, enhance ability might be what you need to get this ability check over the top and succeed.
Better yet, incapacitate the target first ...
... and then stuff them into the bag, and then do the thing with the poles and the empty bag. An incapacitated target can easily be shoved into the bag if they fit at all.
Incapacitated
Or paralyze them... (See Appendix A, Conditions, Paralyzed) ...
... or, knock them out first
You can use the knock out rule from the PHB Chapter 9, put them to sleep, or use other means to render the foe unconscious.
For further shennanigans
Craft or otherwise acquire a bag of devouring, polymorph the enemy into a small beast (snail, clam, slug, earth worm, etc) and then drop the enemy into the bag of devouring. Problem solved. (Thanks to @SumofeDpi for reminding me)