I agree with Felix, but I do know of one trick that might help. Grab your largest floor tom(preferabley 18"), tune it down as low as it can go while still sounding good.
(snip)
Another thought: if you want to try this technique, and you're multitracking the session (vs. going "direct to two track"), record the bass drum as it is, and after the fact, set up this floor tom and a good speaker in the studio. Mic' the floor tom, and record it onto a separate track as you play back the bass drum track through the speaker. This will give you the ambience of the floor tom, but you can control it in the mix, and it won't leak into the other drum set mic's during tracking.
Or just use the BD track to trigger a sample, as Felix mentioned.
But if you really want "...a really deep, full bass drum sound," open the @$%# thing up - no pillows, no foam, nothing inside (well, maybe a felt strip on the front or back head). Don't get spooked by the amount of ring when you play the BD by itself - most, if not all, will get masked by the other instruments when played in the full-band context. The drum can sound this way on its own - you don't need to resort to studio techniques to do anything other than accurately record the drum - just make sure you have a mic' designed for bass frequencies.
