You need to get Roman's like level over 75%. When you start the game, his like level is already over 75%. Just be patient and wait until he gives you a call telling you that he can send someone to drive you.
If you don't want to spend the time hanging out with Roman but don't want his like level to drop, accept what he wants to do when he calls you but then call him back to cancel the plans. That way his like level won't go down.