Insert a noise gate onto the audio track you want to reduce bleed from. Do this with a hardware noise gate unit or a software plug-in, depending on your audio-mixing setup.
Adjust the threshold of the noise gate so that it turns on when the volume of the audio track falls below a certain level. For instance, if you want to get rid of the cymbal bleed on a snare drum track, set the threshold so that the noise gate turns on when the level drops below the level of a snare drum hit, but above the level of the cymbal bleed.
Set the "range" of the noise gate to determine how much you want the gate to reduce cymbal bleed when the level of the track falls below the threshold. A small range will yield less noticeable reductions of the bleed; a large range will yield more noticeable reductions.
Set the "attack" of the noise gate to control how quickly you want the noise gate to begin reducing the bleed once the level falls below the threshold.
Set the "release" of the noise gate to control how quickly you want the noise gate to stop reducing the bleed once the level rises above the threshold.
Adjust the "hold" setting to determine how long you want the noise gate to reduce the bleed when the level falls below the threshold and then rises above it immediately. This will allow for smooth bleed reduction whenever the level of the track is wavering around the threshold.