Can't You Just Ignore the Bank and Go Rogue? You could just form a gentlemen's (or gentlewoman's) agreement with someone and let them drive the car if they'll agree to regularly pay you, and you'll continue to make the payments on the vehicle with their money.
Can I let someone take over payments on my car?
Can you transfer a car loan to someone else? You cannot “transfer” a car loan to someone else without also transferring ownership of the vehicle to them. In most cases, transferring ownership is considered selling.