I don't think they get paid, I believe that they drive a person they have a lot of business with. On the high end of it, Billotti driving Paul Castellano is a good example.
I never understood why Castellano kept Bilotti as a driver once he made him underboss. It doesn't send a good message to the Family and to the other families. It made him look weak. Do you think Neil Dellacroce would have driven Don Carlo ?
Chin Gigante had one of his capo Vito "Bruce" Palmieri drive his wife and daughter when they would go from their house in Jersey to his mother's house in the Village. So that's a captain who is not even driving the Boss but the family of the Boss
To me, the boss's driver should be a made guy but certainly not a capo or administration.