I've heard there's a rental shuttle to the Avis lot, but I've never seen it when I go outside. You can go out of the terminal, across the street into the parking garage and go left following signs for rental cars. Take the elevator to the Avis lot. You can walk it in ~5 mins, so if there is a bus, I'd never wait for it.

EDIT: If you go to Avis.com, search for and find the location, there is a "For More Location Information, Click Here" button. For DCA, it says:

*GENERAL DIRECTIONS*
COUNTER: - AIRLINE PASSENGERS:
Follow Ground Transportation signs to airport shuttle bus. Take the airport shuttle bus to Parking Garage A, follow signs to the Avis counter located on the 1st floor.

COUNTER: - WALK-UP RENTERS/LOCAL RENTERS:
From George Washington Memorial Pkwy: Follow the signs for the Airport. Then, once in the airport follow the signs for the Rental Car Returns & Parking Garage A. Avis counter is located on the 1st floor.

CARS: Vehicles are located on the 2nd floor of Parking Garage A.

RETURNS: Follow signs marked "Car Rental Returns".


AFTER-HOURS RETURNS
Leave the keys in the vehicle & leave the vehicle UNLOCKED (Note: The car returns area is a secure area).


PREFERRED SERVICE
Follow Ground Transportation signs to airport shuttle bus. Take the airport shuttle bus to Parking Garage A. Upon arrival, Preferred Renter's will follow the signs to the Avis Preferred Booth located on the 2nd level of Parking Garage A.



As long as your brother is capable of pulling his suitcase by himself, I'd still walk.