6, 9, 13, 15, 23 and 139 should do it - west along the Strand and up Lower Regent St. Bus stops in central London should all have little plans on them showing which route is taken by each bus that uses the stop, along with a screen telling you how long the next one on each route will be. They don't take money in central London so you'll need to prepay - Oyster card, travelcard, or buy a ticket at the machine at the stop.
But as others have said it's quite a short (and interesting) walk.