Marcella,
I am a big believer in the "teach a person to fish" philosophy. So, let me first directly answer your question, and then I'll provide some advice and tools to help you figure some of this out on your own. Okey dokey?
You are correct that the buses go from resort to park, and not resort to resort. So, you need to use one of the parks as your transfer point.
To get from All-Star Sports to Cape May (at the Beach Club Resort) I would take a bus to either Epcot or Disney's Hollywood Studio (take whichever bus comes first) and then from the park I'd catch a bus to the Beach Club Resort.
To get from All-Star Sports to Chef Mickey's (at the Contemporary Resort), I would take a bus to the Magic Kingdom, and then either take the Resort Monorail (the Contemporary Resort will be the first stop) or, if you are in the mood, walk to the Contemporary (it only takes 10 minutes).
Now, on to the "fishing" part... If you ever need help figuring out timing and routes for WDW transportation, I have listed several very useful resources in
this prior Q&A. These resources include the Unofficial Guide's helpful table of commuting times, and the Laughing Place's helpful trip wizard calculator which provides suggested transportation options between any two locations at WDW. You also might want to
click here to download a very useful map of the entire WDW property.
Hope that helps your navigation of WDW go just a bit smoother. ºoº