Jane, all the locations that I searched for regarding Triumph rentals all are round trip. If a round trip is do-able (maybe do a eastern round trip, with a possible western one another time) here's a link to a outfit that rents Triumphs in Orlando Florida:
http://www.modernclassicmotorcyclerental.com/Site says "fully equipped bikes starting at $49.00".
Good luck with your planning.
