Was the vocal recorded while singing along with the BiaB song? (!important)

For my workflow (assuming the tracks are the same tempo) I would import the audio track into RB on a blank track and see where it ends up.
After doing so, maybe Save As and save it with a different name (so you always have the original).
Then I would open the Audio Edit window (the waveform icon) with the desired vocal track being the selected track.

Using the 2 sets of +/- keys in this window (one for height and one for width), zoom in as much as needed to align the vocal peak to a bar line.

Hold CTRL and tap the A key (CTRL+A) to select the whole track.
Then again hold the CTRL key down and use the mouse to 'grab' the waveform (click and hold left mouse button) and then drag the waveform to line up with the bars. Let go of left button when aligned.

Go back and listen.
Adjust as needed.

If it still fades in/out of sync, things get more complicated .. but still possible.

Make your sound your own!
.. I do not work here, but the benefits are still awesome