No, the merchant do not sell bullets. You have to find the cowboy.
If you land on the dungeon you can play, indeed, but the very moment you go back to the world map you will be dead, so yes, it's a bug, but it doesn't change things that much.
Again, thank you very much! I know the gaint beetle is quite scary (and, if you do not pay attention, it WILL kill you). However, you have to know that, with enough bullets, you CAN actually destroy it!