Well you're still in the right place.
The handlebar clamp is 25.4 mm -- 1" -- still the most common size now. Shouldn't be any trouble matching that. I've ordered from bikepartsusa, niagara, aebike, and others -- there are many good web-order shops -- or go to your LBS and ask.
I have a Wald-made bar similar to the 'Velo Orange Milano' -- http://www.velo-orange.com/milanbar.html
-- a bit more forward than your original bars but preserves the look.
The handlebar diameter (other than at the stem clamp) is 22.2 mm -- 7/8". The brake lever and shift trigger clamps require this size. This is the same as normal MTB size so you should be OK with the clamps. May need to shorten the cables & housings then. For the 3-speed cable, may then need a replacement anchorage: http://harriscyclery.net/itemdetails.cfm?ID=1096
Will you be OK with the same stem? The stem diameter where it inserts into the steer tube is 21.1 mm. Slim pickings in this size, but still some available. There should be at least 2" inserted into the steer tube.
Getting the grips off the old bars: I have success forcing a screwdriver underneath & then squirting some 3-in-1 oil in there & working it around. Maybe the easiest is, if you have compressed air, to use a blowoff chuck in one of the little holes in one grip while plugging the hole of the other grip.
HTH - Good luck & keep us informed!
PS - If the following has never been done -- I'd recommend going all the way -- clean & lube the headset, bottom bracket, wheel bearings. True the wheels and tension the spokes -- a must especially given your size. Not rocket science but especially for a newby will take some time. Oh -- serviceable pedals! -- do the same for the pedals. These Schwinns require a minimum of special tools. This will help your ride live up to the Schwinn reputation for pedaling efficiency and bullet proof reliability and longevity.
Last edited by duffer1960; 08-16-09 at 06:32 AM.