According to the item properties in the DMG, no, it can only be opened from the outside. Specifically, items inside require an action to be retrieved.
(To satisfy those who have asked: the word retrieve, as used here, is a transitive verb with an implied indirect object, usually the same as the subject. The direct and indirect objects of a transitive verb can very rarely, if ever, be the same in English. Therefore, no, something can't retrieve itself, because that doesn't make sense.)
However, YOUR bag of holding does not have to be the bag of holding presented in the book. If you say that it can happen in your campaign, then it can. Never let minor mechanical details get in the way of the story (being mindful of your players, of course).
D&D5 says what it means and means what it says. Don't try to overanalyse it.
You choose whether your equipment falls to the
ground in your space, merges into your new form, or
is worn by it. ... Your equipment doesn’t change
size or shape to match the new
form, and any equipment that
the new form can’t w ear
must either fall to the
ground or merge with it.
Equipment that merges
with the form has no
effect until you leave
the form.
There is no in game definition of "equipment". The OED defines it as "anything kept, furnished, or provided for a specific purpose".
By this definition equipment could be your castle, your rowboat, your bed, your guard dog and your farm as these could all be things "kept, furnished, or provided for a specific purpose". However, in the context of the rules where, among other things, the equipment can "fall to the ground", it must be interpreted as stuff you are carrying.
Anything you wear or let fall to the ground is unchanged and weighs the same. Anything that merges is useless and weightless because it "has no effect".
TL;DR
"Equipment" is anything you are carrying or wearing when you wild shape because ... magic.
Best Answer
Easy peasy
As long as the players can fit through the neck of the bag they can exist inside until you're nice enough to let them out, thanks to the necklaces of adaptation.
Even without them, it would still be possible but how long they can hold their breath would then become an issue.
Just don't die because no one else will know to let them out...
I think using Bags of Holding like this is always a great idea. My players have used a BOH to fly team members across chasms, hide them from magically tracking hunters, sneak extra people into a party, etc.
It can subvert a lot of what the DM thinks might be a challenge for the players and turn tricky situations into slight inconveniences so some DMs may place limits on what can be done.