1. How deeply rooted is clumping bamboo?

Don't know about clumping. Most of the rhizomes of running bamboo are
within the top 12 inches or so (maybe more like 6). You'll find them
easily enough if you start digging and follow the rhizomes.

2. Can mere humans dig up the roots after thoroughly
moistening the soil?

Yes. We dug out a bed which was maybe 5 feet by 40 feet, which was
fairly densely populated with running bamboo (both above and below
ground). Takes some time, and you'll probably end up disturbing most
of the soil. If there are any plants you want to keep in the area,
you'll probably end up digging them up in the process and replanting.

We mostly used a trenching shovel which is durable enough to function
as a pry bar too (unlike, say, a spade).
http://www.rittenhouse.ca/content/im...ing_shovel.JPG
http://www.gemplers.com/ctnp/longhan...ls/G44023.html

This was a few afternoons of hard work, but after that we just needed
to watch for shoots coming up, and dig out the little rhizome piece we
had missed in each case. (we didn't do the "break off the shoot"
technique, as the roots we missed the first time were small and it was
simple enough to dig them out).

3. If not, what kind of "professional" help would be
required -- one hopes not too expen$ive.

You can see if any bamboo nurseries around you would be interested.
At least, http://www.bamboosourcery.com/catalog_sec.cfm?row=4 says "We
also occasionally remove unwanted bamboo free of charge upon request,
if we have time and have a use for it." Don't know if this is common,
and it is clear that there are various catches.

In my experience (with bamboo and other unwanted plants) the key is
spending some time at it and persistence. If you are thinking that a
one-time low-effort treatment (whether chemical, digging, mowing,
tarps, etc) will get everything, it is easy to succumb to despair.
But if you are prepared to get out most of it, and then go back every
week or a few, digging up whatever came up in the meantime, you have a
bit more of a chance.