The dirty little secret of campaigning is that candidates frequently wash themselves with anti bacterial soaps after shaking hands with people. Bush, and all candidates act not much different than germaphobes.
One of the Clinton biographies talks about the “bucket guy” who would be on the campaign trail in the days before pocket bottles of hand sanitizer. He’d be in the limo or the bus with towels and a bucket of soap and water for after the candidate had been out pressing the flesh.