The Schwinn branded Spinning bikes use a standard cartridge BB. $20 will get you a brandy-new one. Use one of those 3M refinishing pads from Home Depot to get the rust off of the flywheel and use a rust reformer and spray paint combo to fix the frame and bars. Then tape the bars with handlebar tape to protect them, and give you a better grip on the bars. Replacement stainless hardware will complete your restoration. If you want a repair manual, go to
www.studiocycles.com and order the one Jeff Wimmer wrote. We just got rid of a dozen of those bikes and replaced them with the newer StarTrac model. Which bike do you have? The Elite (red wheel) or the Pro (black wheel)? If you have an Elite, keep an eye on the SmartRelease clutch on the flywheel. They can be problematic after hard service.
Good Luck