I don't think they are best friends, just part of a very exclusive "club". I think having served in the presidency and understanding how difficult it can be they now have a mutual respect for each other.
Often the outright hostility you see between politicians disappears when they are out of office - especially the presidency - and instead of barking at each other - they find common ground - in many cases - working on something they both agree on - and as odd as it seems - they become friends.
The past presidents club is pretty chummy. The only ones who didn't seem to join are Carter and Nixon. It's looking like Obama may opt out, as his continuous attacks on Bush haven't been matched with many positive experiences, and there are more ex-Republican presidents than former Democrat ones.