Have the crew of the Bebop ever been paid for a bounty?
Yes.

Episode 8:They catch a group of thieves trying to steal a spaceship.Episode 10:(It's never actually explicitly said if they got the money for this one. The guy was caught despite him probably going to get off with a self-defense plea.)Episode 15: They technically collect a very small bounty at the end of thisEpisode 16: It was never stated as to whether they received anything for helping out with stopping the prison shop. However, if you were to assume they did.Episode 22: They do end up catching the teddy bear bomber here.