To be honest, I wouldn't make a special journey just to go to the Bowie shop even though it only takes about 30 - 40 minutes on the train to Waterloo or Victoria.
Would make sure no rain is forecast and see plenty of the real sights of London Town, and maybe even a stage show up there.
Loved it when Sunny Afternoon, Jersey Boys and a few other stage shows in the Leicester Square, Soho area were fairly easy to get good seats, at a great price.