Here's a basic bebop study, looking at how Connie Kay plays the head of Billie's Bounce— we've got the drums transcribed, along with the melody rhythm so you can see how they intersect. Kay was the drummer for the Modern Jazz Quartet, and was sort of a quiet work horse— I've not come across a lot of records with him giving big performances like drummers like to hear. But my listening habits are kind of narrow and not encyclopedic. The album is Stan Getz & J.J. Johnson At The Opera House, from 1957.
The 8th notes here will swing, of course. The cymbal rhythm is played on an open hihat, with a few punctuations on a small cymbal— maybe this is Kay's famous 17" Medium-Heavy. It doesn't really matter— play the cymbal part wherever you want it. Nothing is apparently happening with the left foot. It's likely he's feathering quarter notes on the bass drum, when he's not catching the melody rhythm exactly. He generally stays so close to the melody that there may not be a whole lot of that.
He makes many of the accents with unisons between the cymbal, snare drum, and bass drum, which is a little unusual— that gives a very heavy sound, and he underplays the snare drum a bit on those; the accents are predominantly bass drum. I think rather than making those unisons, you could catch those accents with either bass drum and cymbal, or snare drum and cymbal.
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