Well .. here's a few thoughts ...

What could possibly plug up a bathroom sink drain that even 3 doses of
straight sulphuric acid can't dissolve??? And if sulphuric acid won't
dissolve it, what will, that won't also destroy the pipe (PVC, btw)???

Sulphuric acid ... yikes. First, check that you don't have a mess of hair
stuck in the strainer affair in the bottom of the sink. You can use needle
nose pliers to poke around there and pull up any that might be there. If
that's not the problem, try what's called a plunger :-) to clear the
p-trap. You have to hold a wet cloth over the overflow drain to do this
properly ... best done as a 2 person job. If that does not work, and there's
no "cleanout" (that plug that unscrews from the bottom of the trap) in the
p trap, then you might as well replace the trap with one that has one. I'm
sure you're familiar with abs and its installation. I'd just cut the old
drain at a convenient spot, and install a new trap.

Nothing has fallen into it...it's been gradually getting a little slower
for a while. It's not quite plugged completely...but drains so slowly
that the sink is all but unuseable.

Having said all that, if you have a long run from the sink to the main waste
pipe, the problem could be there ... especially if there's no vent pipe
(that second pipe that allows air in to help with the draining). So if you
do replace the p trap, and there is a long run, maybe snake that run while
you're at it. But you know what ... I'm betting there's a big clog of hair
clinging to the bottom of the strainer in the basin :-).

I don't want to pay a plumbing $100 just to pour something else down the
drain that I can buy for $10. There has to be something that'll dissolve
the clog...but if sulphuric acid won't do it, what will???

I'm open to any ideas that won't dissolve the pipes too.