Make one of these your main groove:
Grab some cymbal rhythms from pp. 10-11 of Syncopation. For example:
Add some left hand filler wherever you like. You could start by adding it on the & of 1 / & of 4, wherever there's a gap in the cymbal rhythm. In these examples I've eliminated the bass drum for visual clarity— keep playing it.
Move the left hand around the drums, play around with sounds/articulations— rim shots, rim clicks, buzzes, doubles. The resulting groove is similar to a Everett Morton type of ska groove, with a mixed cymbal rhythm a la Stewart Copeland. Here's a Morton-esque embellishment for you, while we're at it:
I'll do a few more of these. Like I said, it's a very easy, lightweight little thing, more an invitation to play around with an idea, while learning to be happy playing quarter notes on the bass drum, than it is a hard and fast drill to be rigorously worked out.