I don't think there's anything to the theories, but the name George Bush does turn up twice in the files.
Once is in reference to a CIA agent the FBI briefed about the assassination. It was probably another George W. Bush who worked for the CIA at the time, but he says he wasn't briefed.
The other reference is to a George H.W. Bush who called in on the day of the assassination to say that he had heard someone making threats to kill Kennedy when he came to Houston.
Apparently, that was the future president. I think the conclusion is that Bush had nothing to do with the assassination, but the guy who worked for the CIA and says he wasn't briefed is one reason these theories are circulating.
GHW Bush was running for the House in Texas in 1964. Traveling with Goldwater to airports and campaign events. That’s when I met him as a Goldwater campaign worker. I don’t even recall if he won that year; I was too destroyed when Goldwater lost to care. Maybe Bush ran again in 1966. He did make a call to the FBI or a CIA office in Dallas on the day JFK was murdered. It’s documented, and he called from Tyler, Texas, maybe to establish that that’s where he was. Tyler is 92 miles from Dallas down I20 in the days when speed limits were whatever a car would do. Also there was Love Field in Dallas and a little bitty crummy airport in Tyler. So who knows.