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 you play with.
Specific beats general. So, 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.
So 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 p. 140 DMG:
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.
So 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 (p. 146 PHB) which makes it pretty useless in combat.
So, those are the issues; your group needs to make the ruling.