Here's a little trick I always use when recording bass guitar in a DAW : doubling the track, with a LPF on one and HPF on the other, both separated by a crossover around 250 hz. This way I can add drive on the HPF channel while keeping solid bass frequencies on the other - because the more drive you add, the more low frequencies you lose.
For this video I used an Ibanez with 3+ years old strings, they're almost dead so with new strings tweaking will be necessary.
Preset on AxeChange :
Tweak to your linking !
Note : HPF = High pass filter, LPF = Low pass filter
Edit 26/09 : There's a demo of a newer version of the preset on soundcloud, I replaced the crossover blocks by filters, and I control the crossover frequency with an expression pedal :