I'd start with a low-pass filter at about 100Hz, and experiment from there. Since you are using a microphone, the amount of bass your're getting into the microphone depends on your system and speakers. If you have a system with good bass (or with a live band) you can probably go down to 50Hz or lower. If you've got a system with a subwoofer, just putting the mic in front of the sub will help a lot.
for example, a steady bass beat with someone singing over it would only flash with the bass beat and not with the singing.
You know.... Depending on the music, the bass doesn't always match the beat perfectly either, but it should be closer to what you're loooking for. For example, the kick drum usually gives you a fairly steady beat, but the bass guitar is often a bit more complex. But if you are making a lighting effect, sometimes it's more interesting if the light doesn't
flash perfectly to the beat like a metronome.
I've done some things in software (in my sketch) to improve beat detection. One thing I did was make a delay, so it won't pick-up a beat faster than about 4 beats per second (then as more time goes by, the detection threshold gets more and more sensitive 'till the next beat is triggered). I think more could be done, such as digitally filtering/tuning the "envelope" to favor loudness changes around 4 beats per second.
And, you could make it intellegent, so that once you've found the tempo, you continuously tune it to "expect" the next beat... That's how humans do it... We don't wait for every beat. We get in rhythm with the beat, and we know when the next beat is coming.