Probably not much. They are former Presidents now. They do get their own secret service security details in retirement. I don't imagine they'd need much beyond that.
I don't why some are surprised that these two get along (reading the tone of some of the articles). I would figure that nothing would bond two individuals like having experienced the Presidency. After all, the only person could ever comprehend what a President went through would be another President. I can even see Obama being a lot more sympathetic to Bush in a few years.