You might want to avoid V. D. Lane (as us schoolboys called it :) ) near where Lansdown Road levels out. We were made to run up there in cross-country :(
I went to school in Bath, so know the city well. I always went by train, but was NEVER able to do so without changing at Fratton. From there it was direct though; did your train stop at tiddly Dilton Marsh? In the 1970s it was just a wooden platform long enough for one carriage.
I'll bet you...