I wrote this up after listening to Mel Lewis's history of jazz drumming tapes, where he was raving about the importance of playing time on the bass drum (he really gets into it after 43:30). He basically describes this exactly, for making a syncopated accent with the bass drum, and then going back to feathering. This, together with some other things I've suggested, should make you functional enough to work out your timekeeping voice with the bass drum through playing with people.
Loren Schoenberg, who did the radio interviews with Lewis, has posted the tapes on YouTube— and a lot of other interesting stuff. He's a good person to follow.
Play the rhythms on the bass drum along with the normal jazz rhythms on the cymbal and hihat. Play the unaccented notes softly, but get the timing and coordination before sweating any extreme dynamics. My whole objection to this type of thing is that I don't want to work out vestigial bass drum— I'm not going to work out perfect 1" bass drum strokes in the practice room. It has to be an organic process.