I've heard some theories that he was involved in things, possibly even there in Dallas.
Richard Nixon, on the other hand, caught a plane out of Love Field the morning of November 22. He had a solid alibi for the time of the shooting. Nixon was at the Baker Hotel the night before; Former (?) CIA operative Bush was reportedly was staying at the Sheraton. Barbara claimed they were in Tyler at the time of the shooting, HW went with an “I don’t recall”.
And for fun, trace the links from Bush to the former CIA station chief in Athens to Stavros Niarchos to Jackie Kennedy’s lover Ari Onassis. (Niarchos’s wife was ex-wife of Onassis and the mother of Onassis’s daughter).