Watch the Sweet Notes online guitar lesson by Jeff McErlain from Solo Factory: Chicago Blues
The composite blues scale is a mixture of the major and minor blues scales. I certainly don't think BB and others ever used that name for the scale but they use it all the time. We are in A on this one so our notes would be ABCC#DD#EF#G. That's a lot of notes to think of at once, so don't! I see this scale as a variant of the Am pentatonic scale with some added notes. Most notably the added natural 3rd. We can then add in the 13th which is F# and the 9th which is B. Try adding one of these notes at a time to get the sound in your head.