As you leave the platform, and join the main concourse, turn right. Go past the steps and escalators leading up to Waterloo East station and then look for the escalator going down to the Waterloo Road exit. It's in between retail units 24 and 25 on this map:
http://www.networkrail.co.uk/documents/For%20P assengers/Station%20Maps/4511_Waterloo%20Stati on%20Map.pdf
You come out by a set of bus stops. The 139 leaves from one of those stops. (Unless you've got an Oyster card, or a Travelcard, remember to buy your ticket from the machine before boarding).
Alight on Regent Street (very shortly after passing Trafalgar Square). Turn left onto Piccadilly. The RA is a short distance along, on the right hand side.
Chris