At first I believed that the return of Bruce Wayne happened directly after rip but I've read that it deals with him returning after Final Crisis. Is there any connection between the two stories or are they completely separate?

RIP is right before Final Crisis.

They are connected, but not chronologically tied.

R.I.P, then came Final Crisis, then came RoBW

Both deal with Doctor Hurt though if I'm not mistaken.

RIP leads up to Final Crisis and Return of Bruce Wayne is after FInal Crisis

They are not completely seperate with both being part of Morrison's run. RIP was really the ending of his work on the main Batman title and the Last Rights issues concerning the immediate fallout of RIP and Batman during Final Crisis. The Return of Bruce Wayne deals with what Bruce goes through after the events of Final Crisis and sets up future stories, it plays a role in Batman and Robin vol.1 1-16 and Batman Incorporated Volume 1 and 2 1-present.I hope this somehow answers your question.

I don't want to read all of final crisis, it seems very confusing but I want to know Bruce's part in it since it directly affects TRoBW. Any help?

Read the Wiki: Final Crisis

what is TRoBW?

The Return of Bruce Wayne or The Revenge of Bat Wankers... You pick.