We considered doing the same thing on our recent trip, but never needed to.
We stayed at the Doubletree Oct 30 - Nov 7 and found the DD resort buses very efficient. They were running to the four big parks every half hour so I doubt you would beat that by walking over to the Disney system -- maybe only if you were at the closest hotel and Disney buses ran every 15 min. (Do they? How often do Disney buses run, anyway? Had trouble finding out.) Blizzard Beach buses were less frequent so if the times don't suit your schedule you might look at the Disney system.
Just realize that the buses usually do have to make the rounds of several hotels, so they can't be at each hotel at exactly the scheduled time. For example, an 8:00 bus to MGM would arrive at Doubletree around 8:05; an 8:00 to MK might arrive at 8:12. Once it had been to every hotel, it proceeded very quickly to the park. I suppose your perception of the bus speed might depend on whether your hotel was the first stop or the last stop!
Some of the drivers are better than others at making announcements before you get off to make sure you know the return schedule and pickup point. If they don't announce, ask. It's not difficult. In each of the 4 big parks, pickup is at spot #26 (same place they let you off). Times were every half hour, but changed at some point from :15 and :45 to :30 and :00.
We did walk to and from the Downtown Disney Marketplace area twice in the evenings, but not to catch buses. The closest hotels are Hilton and Wyndham. Doubletree and Best Western are farthest away. The walk from Doubletree was probably anywhere from 10-20 min. depending on your walking speed. We also walked to the early Cirque du Soleil show on the West Side one day. That is a longer walk! DD resorts do run buses to Pleasure Island, but they don't start until 6:00 PM.
The DD hotel buses don't run between parks, so we used the Disney system for hopping around. eg. direct bus from Blizzard Beach to Epcot, monorail from Epcot to MK.
