I've done some pit firing of clay. Commercial clay though. Turned out great, but doesn't reach a temp that was needed to harden the clay enough to my liking. However, I'm sure that primitive potters were not too worried about that. As long as the piece was capable of doing it's intended job, it was good. I have made a few arrowheads from pit fired clay, looked awesome, but not hard enough. Anyway, there is an easier way to make a bowl. Flatten the clay and stretch it out as much as possible, like you would flatten a pie crust or cookie dough. Find a nice round rock, and use the rock as a mold, let it dry, then fire it. Before the clay is completely dry remove it off the rock, it should be still a little soft, but firm enough where you don't need the mold anymore. One more trick, while it is air drying, lightly cover it with something. Most clays will crack if they air dry to fast. Well good luck, and we would love to see a few pics.
Tattoo Dave