So tonight we see Bobby overhearing Jane and Cindy's conversation about Ben and protecting Bobby. Then he goes to the police with the wallet and phone.

Does he realise now he killed Lucy and is trying to frame Ben?
If not, why is he taking the stuff to the police?

I think he believes Ben should be punished as he believes Ben killed Lucy

He just Wants the killer caught.

I think, or at least hope, that he thinks it is Ian or Jane at the moment, but following his confrontation with Phil, the penny will drop, and he'll either be like "Oh god, what have I done?" or even more psychopathic

The only bit of the conversation he heard was Jane saying she wasn't going to drop Ben in it, as much as she'd like to. He thinks Ben killed Lucy.