From what I can seen on the Schwinn website, athrowawaynic is correct that it is a 25.4mm clamp diameter. Handlebars with a 630mm width are most common and easiest to find. Check to see if there is a bicycle co-op in your area that should have plenty of used ones.

Swapping out the bars is relatively simple. You have to remove the grips which are just slipped onto the bars. Use a thin screwdriver or 2.5mm allen wrench under the grips and spray in water, Windex or alcohol (but don't use an oil based lubricant). Pull out the screwdriver and the grips will be lubricated enough to twist off. The shifters/brake levers are secured with a bolt of some kind. Since they are single unit, there should only be one. Slide them off. Loosen and remove the two bolts on the stem (in the middle of the bar) and the handlebar will come right off.

The replacement is just the opposite of what you did to take it off. Snug the stem bolts down so that the handle bar doesn't twist and tighten the brake levers enough so that they don't move. You don't need to be a total gorilla about it but make sure the bar doesn't twist before you ride.

If you have some hairspray, spray it inside the grips and slide them back in place. This will keep them from turning. If you don't have hairspray, rubbing alcohol (or even drinking alcohol) will work but it takes longer to dry.

It sounds more complicated than it is. Good luck