It sounds from this description like you’re trying to get a sound that the instrument isn’t best suited to.
If you (and/or the bass player) are happy with the sound from the amp, then you can DI from the bass head (rather than a DI box in front), or mic the cab.
If neither of you are happy with the sound of the bass, then the solution would be to change the bass.
If the bassist/MD are happy, and you’re just trying to make it sound like something it isn’t, I’d say you need to rethink the mix and work out how that sound can work for you.
I hope that helps!