Rule interpretation in general
There are two points to remember when looking at an ambiguous rule:
Your group, with the DM as final arbiter, decides the ruling for the rule. So, you need to establish what this is for each group that you play with.
Specific beats general. Start with the most general rule you can find and see how the specific rules change this.
Armor resizing in particular
For your issue, start with PHB p. 145 (ignoring the optional part because it makes no difference to the case at hand)
Variant: Equipment Sizes
In most campaigns, you can use or wear any equipment that you find on your adventures, within the bounds of common sense. For example, a burly half-orc won't fit in a halfling’s leather armor, and a gnome would be swallowed up in a
cloud giant’s elegant robe.
There's your general rule: no armor that fits a PC race (size S or M) would fit a bear (size L).
Wild Shape (p. 67 PHB) says:
Worn equipment functions as normal, but the DM decides whether it is practical for the new form to wear a piece of equipment, based on the creature’s shape and size. Your equipment doesn’t change size or shape to match the new form.
No help there; the armor will be too small and the wrong shape. In addition, there is a ruling that has to be made right here: is it practical for a bear to use armor even if it is the right size and shape? My ruling would be yes but your results may differ.
Now from DMG, p. 140:
In most cases, a magic item that's meant to be worn can fit a creature regardless of its size or build. Many magic garments are made to be easily adjustable, or they magically adjust themselves to the wearer.
The ruling needed here is does the hide armor a) need easy adjustment or b) magically adjust itself. If b) then all is easy, if a) then the druid may need to allow it to drop to the floor and then get some assistance to put it on which would take 5 minutes (PHB, p. 146) which makes it pretty useless in combat.
Those are the issues; your group needs to make the ruling.
This exact question was answered just this Friday in the most recent FAQ posting on paizo's site.
Wild armor and other transforming armor: When I use a wild armor and gain the armor’s benefits, what restrictions, if any, apply to me? In general, when I transform with a polymorph effect and some of my gear melds into the form, what restrictions do I have for melding with large amounts of heavy gear? What about other types of transforming armor?
If you were in medium or heavy load from encumbrance before transforming, you continue to take those penalties in your melded form. Otherwise, ignore the weight of melded items and calculate your encumbrance in your polymorphed form entirely based on non-melded items. When wearing melded armor and shields, if you gain no benefit from the melded armor, you still count as wearing an armor of that type, but you do not suffer its armor check penalty, movement speed reduction, or arcane spell failure chance. If you do gain any benefits (as with the wild property), then you do suffer the armor check penalty, movement speed reduction, and arcane spell failure chance. This also applies to all other situations where you or an armor transform: you always count as wearing an armor of that type, and if you gain any benefit at all from the armor (such as mistmail), you apply the armor check penalty, movement speed reduction, and arcane spell failure chance.
It can be found HERE
Best Answer
The rules are intentionally silent, so you have options
The 5e does not have strict rules for this particular situation. It's a game about battles, heroes and monster slayers, not about pet carriers abusing their pets. The general rule for all corner cases — it's up to the DM to decide. The game developers suggest to "go with what's best for your story":
If you are the player, ask your DM. If you are the DM, choose one from the four possible outcomes and stick to this ruling for the rest of the game: