Hello, Carol,
Truly, the easiest and fastest way to get from one resort to another is by taking a taxi, which Bell Services can help arrange for you. However there is the extra cost associated with that, so you can still use Disney transportation to avoid that extra expense.
To go from resort to resort, there aren't any direct buses. You will need to use a park as a hub. For example, if you are having breakfast at the Polynesian Resort, you can take the Magic Kingdom bus from your resort. Once there, you can transfer over to resort monorail to get to the Polynesian Resort.
If you'd like, I can "map" out more specific plans for you if you
send another question my way that includes the resorts you are having breakfast out to help you pick the shortest/quickest route. I'd be more than happy to help!