I'm a non driver, I tend to get a wee bit further a field on my bike but I doubt you'll be packing that either
Given your limitations I'd suggest Pitlochry or Dunkeld / Birnam. River fishing on your door step, good local bus service (not plentiful but they do run to time) to get you to some lochs and also the train to take you up to Rannoch and its fishing.
The other spot that springs to mind is Peebles for some fishing on the Tweed, lochs are a bit more difficult round there.
Then there is always the west highlands, find a cottage by a loch there are a few, but getting there might be a problem.
Norm