I think being ex-presidents gives them a lot in common. It’s a very unique position in American life. You’re supposed to still be dignified and attend state events, there are a lot of unwritten rules about what you can and can’t do, you have to live with constant secret-service protection, and having been a president no doubt gives you an insight into the pressures and needs of the job that other people don’t understand.
How much you want to bet that when Bush 43 leaves the oval office he becomes very chummy with Clinton? It won’t be too long before the two of them are the only ex-presidents around - Gerald Ford is in poor health, Jimmy Carter is really old, and George Bush senior isn’t exactly a spring flower either. It’s entirely possible that by the time Bush leaves the oval office there will only be on or two other ex-presidents, and before the next president leaves office we could be down to just George W. and Clinton. And both being relatively young guys, they could be around together for another 25-30 years, considering the kind of care they get. I expect they’ll have a pretty close relationship.