Do you have a recording of what the issue is when you record your bass guitar? Are you going through any kind of pre-amp or amplifier? If not, and you don't have any impedance matching, you very likely will get a weird sound.

Honestly, if you play bass, you are going to be disappointed with just about any VSTi. Except Trilian. But that's outside your budget.

I went down this road, downloaded every soundfont I could find for precision and jazz basses, got a couple sample sets. All disappointing. That's when I decided to teach myself bass guitar with an actual bass, and a Behringer Bass V-amp Pro that I bought off of Craiglist for nearly free (the guy selling it said he didn't like how it sounded - well, I found out it needed a new button cell inside. Couple bucks later, boom - literally).

I have never looked back. Replaced the V-Amp with a Zoom B3, and have added an Ibanez 5 string to my arsenal.

You mentioned your bass, but you didn't mention how you are trying to record it.