why did bilbo want to escape from the cave

Do you mean Gollum's cave?

This question is simple, first of all, it wasn't Gollems cave. So, basically what happened is Bilbo left to go give the Arkenstone to Bart. Then he gave it to Bart so that Thorin and Bart could negociate peace terms. Then on the way back to the cave he ran into Gandalf who said "Well Done, Mr. Baggins." Then after when he got back, he revealed to Thorin that he gave the stone to Bart and he got pissed.