The World's Fastest Indian
Once in LA, Burt purchases a cheap car and fabricates a crude trailer for his heavily modified 1920 Indian Scout motorcycle. His mechanical skills impress the car salesman (Paul Rodriguez) so much that he's offered a job. Burt declines and heads off to Utah's Bonneville Salt Flats for Speed Week.
After some road trip adventures including some mechanical break-downs, romance, and help from a wise Native American for his prostate conditon, Burt arrives at the salt flats and is denied permission to run his bike-- he has not registered and his old bike does not pass its safety inspection.
Burt's charm and wit win out in the end, and he is allowed to run his 1920 Scout in an official time trial. He rides his bike to a speed of over 200 MPH setting the land speed record for V-Twin motorcycles with engines of less than 1000cc displacement-- The World's Fastest Indian.
The movie's post-script notes that Burt returns to Bonneville 9 more times and breaks his own record repeatedly. His records still stand to this day.