There's a *lot* of energy in lower frequencies. I can think of two ways to deal with it.
Compress the bass track after you've recorded it, and then it's much more manageable in terms of raising the volume to where you want it. Try ratios like 3:1 with a threshold of -10 dB for a start. Increase the ratio or lower the threshold if you need to squash it some more.
EQ out the lowest stuff that you can't hear. On bass you can cut everything below about 50 Hz.