Even in foreign countries he travels in the official limo, they fly it in on a 2nd plane. In 3rd world countries they may even fly in gas and jet fuel to make sure they get good stuff. And if they buy local gas or jet fuel they test it to make sure it is OK.
Air Force One is orders of magnitude safer than the run of the mill airliner though. It goes through maintenance procedures after every flight that a commercial plane goes through maybe once a year. Any maintenance problems - even a small leak in the third backup to a minor hydraulic system will be repaired before the plane takes off again, or they’ll use the backup plane.
Air Force One gets once a year maintenance after every flight? Do they really have time to do that? Sometimes it gets used every day or 3 or 4 days a week. And can they do all that maintenance when the plane is in Europe or anywhere overseas?
I just watched part of Barack Obama’s appearance on the Tonight Show from yesterday. He told a story to describe the extent of the “bubble.” The other day, his plane landed in Southern California and from the airplane he could see the fairgrounds where he was to hold a town hall meeting. He suggested that they walk there, but the Secret Service said that it was too far, because it was about 750 yards (about a five-minute walk).
But he added that the SS let him walk back to the plane.
I do remember a show on Air Force One that described the painstaking maintenance the plane goes through, and that it’s easily the most maintained and inspected plane on earth. It also helps that there is in fact, two identical Air Force One planes that can be used interchangeably. They also replace parts at the first sign of any wear rather than going through the typical number of cycles a normal commercial jet would go through. In short, they like to play it safe. 
I’ve been overseas and recently was back home in DC and rented a car. It was the first time I had driven in about 3.5 years. By the time I left the lot and was on the highway, I was totally back in my drving mode, including trying to find the clutch on my rental with automatic transmission.
The town hall meeting was just a cover story.
He actually went to the fairground to drive a bumper car.
ISTR a story about Clinton making an appearance at a car collectors’ show (or something) and driving some vintage convertible for a few feet.
Gods, how I hate when I get in my wife’s car and right before I start it, I stomp on her brake pedal and think to myself, “WTF? My clutch feels funny.”
I also have to constantly remind myself not to look for the clutch while driving (or bad things could happen).
Here is a story from seven years ago describing GW Bush having a thrilling time in reverse: