There are 2 level 1 BF keys in the first act, one in the starting cell block (partly hidden behind steam and hanging chains) and one you can't miss another couple levels past the pit level. Shortly after you find the second key, you will be able to get back to the first level again. If you don't need BF access right away, you can just keep going with your original game.
Kiya's BD demo
screenshot walkthrough/spoiler (first level of the game)
BTW, higher level BF keys will open everything up to their level. Even if you miss the level 1 keys entirely, the level 2 key would open the first 2 dungeons. Leaving the lower level dungeons too long may reduce the experience points you get for killing monsters, though (experience drops the higher your level is, until at 8 levels above your opponent you do not get any).
The locked barrel by the kitchen likely needs Lockpick to open (I don't recall a locked barrel there before that skill was fixed).