I can walk it in 30 minutes. By bus, it is about 15-20 minutes. That part of London is sufficiently congested, a bus will get you there almost as fast as a taxi.

Whether you walk or take the bus, you go down Oxford, then down Regent to Piccadilly - and from there can walk to the theatres on Shaftesbury or Leicester Square. The same bus will go on to Trafalgar Square and the Strand, if your theatre is in that area.