Bush used the event's venue, Lyndon Johnson's presidential library in Austin, Texas, as the starting point for his suggestive joke.
"Former presidents compare their libraries the way other men may compare their, well ...," Bush said to laughs.
Bush said he wondered how the famously profane LBJ "would have handled that."
"He was a funny guy at times," Bush said of Johnson, according to the Houston Chronicle.
Here's a video recap of Bush's remarks. His dirty joke comes before the 50 second mark.