My grandson age 27 just finished the entire Trace on an old, heavy bike, loaded with panniers. His friend pulled a Bob Trailer. The section you will be riding is hilly, but you should be able to do it with almost any kind of bike, especially if you're only riding for a day or two. Unless you are exceptionally strong, young, and maybe a little bit foolish, longer tours on a mountain bike like what you have will wear you out.