The "Flee" option will be your best friend in this situation. It is useless to avoid the fight since the bears are blocking your path, but you will be able to delay them. This gives you plenty of time to manage your inventory and heal your group's health and juice. Also remember that you will be able to use Heros Cook ability to heal you out of battle without any limitations (besides juice). Always do prefer to use these Items out of battle because otherwise you will burn through your snacks in no time.

In round one you let Omori use Mock, let Aubrey attack normally, let Kel use Flex and Hero massage the bear. The bear will attack first and there is a chance that he will oneshot one of your characters (Kel is most vulnerable to this due to is low early/ mid-game HP). If he does, you should consider fleeing to regroup. If your characters survive, use the "Look at Kel" option as Aubrey attacks to make both her and Kel angry.

In the second round have Omori attack (normally), have Aubrey use Headbutt (since it's a super cheap yet effective attack), has Kel use Ricochet (or another high DPS ability in the worst case let him attack normally), and have Hero use Cook on whomever the Bear decided to attack the last round. At this point, you don't have to be worried about the bear's attack anymore since Omori used Mock on them the last round, making the Bear's attacks essentially do nothing to you.

In round three and onwards, you let Aubrey still use Headbutt but let Omori and Kel attack normally as to not waste too much juice (remember to manage your resources, there are still a lot more bears to come). The bear will keep getting mad from time to time, so make sure you have Hero ready for his Massage ability, to minimize damage and to spare finite resources.

After the battle is won, remember to flee from the next one to buy yourself time to heal and regroup.

This is all the advice I can provide. If you don't have any snacks on you will probably have a way harder time, but as far as I know, there is nothing more you can do to better your chances. I hope this guide was helpful, and prevented you from losing your mind. In the end, I have to thank the r/Omori Subreddit that helped me through my first bear attack and taught me these strategies.