Yeah, Cohn's career will take a hit if Bundy has the same proclivities as OTL, to put it mildly...
But will Bundy become a serial killer ITTL?
He is still a psychopath, yes, but psychopathy alone doesn't make a serial killer. From what I understand, the two events which triggered his murderous activities were:
1) finding out that his "sister" was actually his mother
2) being rejected by Stephanie Brooks
If you can avoid these two (or just one? IMO it is inevitable that he finds out who his "sister" really is) events while also avoiding other traumatic experiences, perhaps he can be prevented from becoming a serial killer?
However, Bundy was still highly disposed to criminality even before he became a serial killer-- he stole, trespassed, loitered, etc. as a teenager, and as a psychopath had little or no regard for the rights of others.
He will end up in jail one way or another, methinks. The only questions are:
1) from how high will he fall?
2) who will he drag down with him?