We used the buses from SSR to go to MK, MGM and Epcot. Travel times are similar to OKW- except that there is only one stop right now- so the trip may be even faster than the OKW routes at this time. There will eventually be three stops, plus a possible stop at the Carriage House. The bus stops are in a convenient loop around the resort- so there will be minimal bus traffic at the resort.
They do not yet have the SSR bus stops marked at all parks. At MK it is stop #9 (across from the OKW stop), at Epcot it is #3 (with OKW). (I can't remember the stop at MGM).
The drivers are still getting used to the new resort. The buses are pretty empty right now with only one building open, but will pick up as more open. The bus is NOT shared with OKW - it is dedicated to SSR.