Gosh, sorry Op, I didn't realise it was quite so far. I've made the walk before as far as Mc Donald's from ASMu and it seemed fairly quick. Last time I was staying at CSR we almost walked to BB as the bus was taking a while. In the end we waited and a bus showed up. Disney do seem to find a way of looping pathways around the longest possible route, all beautifully themed of course.
My slight hesitation in taking a water park bus later in the day is they seem to be few and far between in the middle of the day, plus the TL bus takes so long if you're before 2pm but after 12pm and have to go via DTD. I know some resorts combine the AK bus with BB but I'm not sure which order they make stops or whether this is just some of the time, I would imagine it's not during peak times but maybe during the quieter times.
At least with the All Star Sports option you are likely to be on your way pretty quick if you don't mind the walk. Disney World does not lend itself to going anywhere quickly, it's as if the whole place is designed to slow you down. Getting into Magic Kingdom is a great example of that, at every hurdle you are slowed down.