Yes, there is a path that takes you over by the old bus stop area. How long it would take would depend on which section of SSR you are at. If you were in the Grandstands, that’s the farthest. We stayed in carrousel last time and we walked once and took the bus once. It took us about 20 minutes to walk there. Congress park is the section closest to the path.
If you're in Grandstand/anywhere else you could also just walk up to the boat dock (outside of bad weather) and take the boat there and back. From anywhere in the park though we've found it to be a nice walk.