I am sure we could engineer somethiing, but why not use a commercial gate? Some have a side chain input so that some other signal can control the gate. Gates are adjustable for release and other parameters. Now all you have to do is trigger it.
Is your bass drum mic'd into the PA? Got an insert on the channel? Or an AUX send you can use for this? Just send the kick drum to the side chain jack of the gate. Voila.
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A piezo sends out a pulse when hit. Plug your trigger into an amplifier and listen to it. I'd be willing to bet the3 raw piezo signal would be capable of triggering the side chain input of a gate.