Here are my B-spec observations:
There is a limit to how much your B-spec driver can learn from one car on one track. If you keep racing the same track with the same car for easy money, he will stop improving at some point. Give him a different car and a different track and progress should be made again. If he doesn't improve any more, try a layout he doesn't usually race (i.e. a Ruf - RR) and he might find room for improvement there. Wether this helps his skill in non-RR cars is not sure, but it might.
A more powerful car will earn him more skill than a suzuki cappucino in a given race. If you find your driver hits a ceiling, buy a fast car, tune it to ludicrous output and have him race that for a while.
LET HIM LOSE. The fastest way to have your driver improve is give him a challenge he can't take. When my driver had 2k skill points, I gave him the 642bhp audi le mans quattro concept and let him do a championship. He finished 5th or 6th in every race, but gained almost 3000 skill in the process. So if you gave him that badass tvr with 600 bhp and he sticks it in the gravel trap in every race, don't abort the race. Let him suffer, and he'll be a lot better when he crosses the finish line.