Walking takes about 35-40 minutes on average. Never got the bus myself, but the Union run a bus service every morning from the top of Hollybush Lane which gets you in for lectures. It was there quite often when I went past, so you shouldn't have to wait for it.
Badock's got a separate music room in the main building, although I only went in once and I can't remember what was in there apart from a piano. There's a good piano in the dining hall too, which I've heard people playing - it got played at the formals too.