I agree on the above post about exporting the song to a DAW and then recording your vocals there. I use Reaper here but there are other ones. A bit of a learning curve, but you don't need to learn everything at once and just a basic mix with a BIAB file and your vocal will be pretty simple.

Export the BIAB file as a WAV file though, not an MP3. You want the quality of that file to be as good as BIAB can produce because you are not done yet, you still need to mix in your vocal.

When you get more adventurous you can export the BIAB file as individual tracks, that will give you more control over the mix. But for now, rely on the mix BIAB has given you, they are not bad out of the box if you are using one of the BIAB styles.

So, after you have your BIAB as a track in your DAW, go ahead and record your vocal on another track.

There are many VST plugins you can buy specifically designed to work on vocals. They basically include all the effects you would normally put on a vocal, compression, EQ, reverb, delay, etc., all in one package, and they will typically come with a lot of presets that will sound good with little or no tweaking. Later you can experiment with building your own effects chain for vocals, but for now keep it simple.

And most of all, have fun!