From the 'Getting Here' page of www.southbanklondon.com (website of South Bank Marketing Group - part of SBEG)
South Bank is a stunning riverside stretch centrally located minutes from Trafalgar Square, Covent Garden and The Houses of Parliament. The area is well-served by public transport and car parking, and is the perfect place to explore on foot.
Needless to say there's no advice to encourage people to get here on a bicycle.