First of all since you are close to Disney Springs it should be pretty easy for you to catch a bus to any of the resorts around property so you won't have to do a bus transfer from SSR to a Park to another resort bus.
As for TS breakfast options here is a small list of great places that aren't too far away from SSR and do not require a park ticket
Ale & Compass (YCR)
Olivia's (OKW)
Trattoria al Forno (BWR)
And for Brunch...
Homecomin' (DS-L) Sat. - Sun.
House of Blues (DS-WS) Sun.
Maria and Enzo's (DS-L) *
Paddlefish (DS-L) Sun.
Raglan Road *
STK (DS-L) Sat. - Sun.
* If days are not listed I would suggest calling to find out the restaurants schedule as I could not find any listed