There is no real way someone here can give you a price that you can rely on. Large metropolitain areas and professional shops with well established luthiers will be a lot higher than a rural area with lower overhead and less brand name luthiers.
Look at what you are asking and try to price it based upon a shop rate:
-The fingerboard has to be
safely removed with no finish or wood damage
-any new shim or fingerboard fabricated and glued on
-the old fingerboard has to be re-installed and then everything cleaned up and fine tuned
-Finaly, all of the setup will have to be gone over and likely the fingerboard getting a light dressing and such because the whole setup will be off a bit due to the invasive nature of the work and any moisture added during the removal / re-do.
Given all that, I'd guess you would be hard pressed in Los Angeles to get it done for less than $600; possibly double that, depending upon the shop. As an additinal note, regardless of your current perception of the neck stability, if the fingerboard was coming off for any reason, I would add a couple of carbon fiber beams to the neck if it was my personal bass. Perfect timing and you'll notice a difference in both stability and voice.
j.
www.condino.com
www.kaybassrepair.com