Bike. I do this every day - through Dulwich Park, down Burbage Rd, Half moon lane, Dulwich Road, Brixton Water Lane, Effra Road, Acre Lane, Clapham Park Road, clapham Common north side, Elspeth Road (via the crossing) Latchmere Road, Battersea Bridge rd. Takes me about 20mins+/- dependant on traffic, weather etc. Not sure about your level of fitness or riding speed but it's definitely preferable to any PT routes. Driving it would be a nightmare as Herne Hill Jct is very congested ATM as is jct of Latchmere Rd & Battersea Bridge Rd.