I'd agree with the poster above, the alternative to the small vertical scar is raising the horizontal scar which is not aesthetic. If a patient does not have sufficient skin laxity to allow the surgeon to remove the old belly button scar (or commonly the navel piercing scar), then closing this as a short vertical incision heals well and is sometimes imperceptible. It's also safer than trying to close your horizontal scar under too much tension. Hang in there, I suspect you will be happier with this when the scar heals/fades (though this is hard to say without a picture). Another alternative is to wait a few months, because when the skin stretches, this scar can sometimes be pulled down to the horizontal scar and removed. Best wishes!
Yours is not an uncommon scenario, as many patients do not have enough laxity above their belly button to allow excision of the hole where the belly button was during a fully tummy tuck. The only option besides closing the hole as a small vertical incision would be to bring the entire abdominoplasty scar up to that level -- not an aesthetically pleasing choice. At this point you simply have to wait and see how it heals. I have found that in many cases the vertical scar is barely noticeable. Hopefully this won't take away from the improvements that you should see from your abdominoplasty. Don't give up hope on your bikini just yet!