at the time it appeared to be primarily because Bobby was legitimately concerned with Sue Ellen's well being and protective of her and felt that Cliff initiated the affair simply to get at JR with no regard for any of the hurtful consequences. There's kind of a "sanctimonious hypocrite bully Bobby's the *real* bad one" vibe here, but other than that temper (and we can see where he got that from Jock), he was pretty pure and noble in the early days. There's no hint of any other motivation during that intense scene he had with her in Fletcher Sanitarium.
Also, he probably felt that Cliff doing something like that escalated the Barnes-Ewing feud and made his marriage to Pam more difficult.