AFK Method:
Make sure you have a wired controller so it doesn't disconnect.
Solo > Time Trials > Any Track/Driver
Drive past the line to start the lap timer and then slow the car to a stop. You can leave your car like this indefinitely and the track time will continue to go up. You can track your progress from the achievements tab in the xbox guide.
If you need to quit out, you don't need to finish your lap, you can just end session from the pause menu.