There are a large number of bus services which stop in the vicinity of Waterloo or Westminster Bridge Road (both accessible to SEA LIFE London Aquarium.)
For Westminster Bridge Road, take the 12, 53, 59, 76, 148, 159, 211 or 341.
For Belvedere Road (just behind SEA LIFE London, parallel to the South Bank), take the 77 or RV1.
For York Road (next to Waterloo and behind SEA LIFE London) take the 211, 77 or 381.
Many other buses stop in Waterloo Road, which is a few minutes walk from SEA LIFE London Aquarium. These include 1,4, 26, X68, 76, 168, 171, 172, 176, 188, 243, 507 and 638.
For more information visit the Transport for London Journey Planner website.