I've done some driving on an AFB, working as a vendor doing installations (Robins AFB, Georgia, if anyone cares). Before being able to go on the base at all, I had to spend some time having them take down all my info, show ID, etc. Then I got a vehicle pass, which (in theory) allowed me to drive between either of the two closest entrance gates and the building where I was working. The MPs at the gate checked vehicle passes and sometimes IDs every morning. This was during Desert Shield and Desert Storm, so pre 9/11 but leading up to/in a shooting war.

I doubt that an MP will be able to let you go on base since you have no business there. The CO would probably be able to override this, not sure why he/she would but it's possible. However, assuming that happens, it might not be the time-saver you think. You WILL wait your turn in line at the entrance AND the exit (no lane-splitting), and you WILL ride within the absurdly low speed limit, and you WILL obey all traffic regs to the letter.