Placing a bag of holding inside another bag of holding opens a gate to the Astral Plane, as discussed here: Is it possible to stuff a Bag of Holding inside another Bag of Holding?
Can I use misty step to get away before the gate has opened? For example, a character runs toward a monster, puts one bag of holding inside another bag of holding, and uses misty step to avoid being sucked through this gate. Does this work?
Here we assume that a bag of holding is a “similar item” that creates an extradimensional space, per its description (as suggested in the answer above).
Best Answer
The effect happens instantly upon one bag entering the opening of the other (see other answers for details of that reasoning).
If you want to Misty Step away, you need to create some kind of time delay. e.g. place one bag on the ground and drop the other bag from waist height as you Step.
Presumably a DM would get you to roll something to get the timing right and not miss. A DM might also require you to spend your Action fiddling with 2 bags, and give an aware enemy a chance to kick away one bag on the ground. (See discussion in comments).
Note that any spell with a 1 Action cast time can be Readied, holding on to the energy to release at a chosen moment (as a Reaction), so you could do this with spells like Dimension Door or Teleport (like Misty Step both have only verbal components so you could have bags in both hands while casting). But not Misty Step itself because its cast time is 1 Bonus Action.
Readying a spell has the advantage that you know you're safe from Counterspell; the window of opportunity was during the Action to cast, not while releasing the energy. Having Misty Step counterspelled after you drop the bag could really spoil your day. RAW, doing it this way to make the timing easier and safer might cost you your reaction (reacting to the bag starting to fall).
You could also use Mage Hand or Telekinesis to drop one bag into another after throwing an open bag out near the bad guy, have a familiar do it, or any number of other ways to avoid needing to bamf away yourself.
Or build a projectile with two bags, with the back one attached to a weight, and the front one held open. So when it hits something, the weight forces the back bag through the opening of the front bag. Similar to a nuclear bomb mechanism that brings together two pieces fissile material. (This idea has been suggested and discussed before).
If you didn't prep such a mechanism ahead of time, using gravity for a "fuse" should work.