Oh I like this topic! You don't have to own a plane to ride on one.....it's called charter.... just like Enterprise, "we pick you up"..... CALL ME! There are others, that have not been mentioned here, whom I've seen with my own 2 eyes at the airport I work at, or I've seen them scheduled via flightaware.
I will say, the actual names of many many private aircraft owners and those who use them are well protected and kept confidential, through chartering, aircraft management companies, putting them under LLC's, etc. What so many people fail to realize, and it is an ongoing battle with aviation advocates, is that these things - especially at this level are not luxury items like the media and the President like to make them out to be in order to call out large corporations for tax implications - they are nessecary tools of the trade.
I find it ironic, that Air Force One is never mentioned in those debates, and I also find it interesting that people will gripe because they find out a CEO and leadership team of a multi-million dollar company flys around on a private plane.... yet it's OK when an air ambulance has to transport you back home after you (God-forbid) get in a car accident while on vacation and your health insurance company will pay for it.