My advice is based on a fairly long trip (about 10 days and getting around on tube & buses). I don't know how I stumbled across this particular version of a London compact bus map, given the dozens of brands, but I'm very happy I did.
LONDON BY BUS is very compact (only about 2" by 5" folded !). Unfolded, one side is a schematic map of all buses across a very large area: from east of Chelsea (Putnam, Hammersmith) on the east edge, to Canary Wharf on the right edge, and up to Hampstead. It gives you the best shot of figuring good routes across town that take two (or, god knows, three) buses. (Actually, probably anywhere you usually want to connect is likely 2 buses.) The flip side of the bus map is a somewhat schematic map of main London (from Hyde Park to just past Tower of London/Whitechapel.) I referred to these maps constantly and it was handy to have one shirt pocket source that was so compact. A standard central London tube map is on the back cover.
THAT SAID: You will want to have a fully detailed map (all streets not just main ones) in your purse or backpack. There, you have two alternatives. Either (A) a full folded map (which probably unfolds to 2x3 feet and is awkward to use on a streetcorner or at a cafe table) or (B) a booklet-style map book (which is good, but you'll sometimes be on the edge of two pages and flipping back and forth where map Page 12 connects mysteriously to Map Page 28). Either way, your full map (or booklet) should have bus routes numbered on it, although you'll find LONDON BY BUS very much easier for planning routes than trying to track teensy bus numbers across 2 feet of map or several different pages of a booklet-style atlas.
There are other mini pocket bus maps in London tourist shops not dissimilar to LONDON BY BUS and many brands of both full-size 2x3 foot maps (choice A) and booklet-size atlases (choice B). My LONDON BY BUS is Oct 2010 so that is good.
For a booklet: I carried London MapGuide by Middleditch. Any booklet would probably be ok but Middleditch was enhusiastically well reviewed on Amazon. Knopf Mapguides London is a small attractive book with fold-out regional maps and multi purpose text about major landmarks, but Knopf omits bus numbers which I found frustrating. Both are light booklets.
One drawback of LONDON BY BUS, it covers a huge area so it is a schematic bus map. Occasoinally it was hard to tell exactly which smaller street a bus was on. that's why you want a big map too. However, LONDON BY BUS lets you see the whole bus system quickly which is a major plus if you are new to the city.