Depending on how you work, Biab may not be the best thing. Real Band may be better.

Biab is designed to create backing tracks for you, not for you to write your own. You can control somewhat how this is done by creating your own style that uses a simpler bass or using one of two tracks that can be recorded to, Melody and Soloist. The problem is if you want the melody track for the melody and you're using the soloist, then you're stuck. If you don't need one of those tracks you can write your own bass track to there and mute the Biab generated bass part. The melody won't regenerate and if you don't have an actual soloist set up in the Soloist window the soloist won't regenerate either.
The other way is to let biab generate the bass track then go into editable notation view and rewrite the part. Then as Rachael said you must freeze it assuming you have Biab 2010.5 or 2011 you didn't say what version you have. The problem with that is you can't make any other changes to the tune. You might decide to add or remove a chorus, change styles, whatever. That frozen bass track won't change and that may or may not be a good thing.
The way I work and YMMV of course, is I would do this in Real Band again assuming you have it. You have 48 tracks to play with and this is what it's designed to do. You can use RB to generate several different Biab bass tracks using different styles, you can edit any or all of them, cut them up, paste them back together and when you have one you like, it's there right in front of you. RB is a linear recorder, all the tracks are visible, if you add or delete something it's nothing to either cut it out or do a copy/paste to add it in.

Bob

Biab/RB latest build, Win 11 Pro, Ryzen 5 5600 G, 512 Gig SSD, 16 Gigs Ram, Steinberg UR22 MkII, Roland Sonic Cell, Kurzweil PC3, Hammond SK1, Korg PA3XPro, Garritan JABB, Hypercanvas, Sampletank 3, more.