OEM brushless motor? Are you sure? If it's brushless I can't imagine it's oem.
http://www.electricscooterparts.com/speedcontrollers36volt.html
That's a tough bike to research. I find no schematics, no parts, specs, etc. And no sign there was a 36v, only 24v comes up.
Schwinn makes me expect it to be Currie parts. If you have an oem controller, I expect it's the same controller you find on other Currie bikes/scooters. You would have either a 5 pin http://tncscooters.com/index.php?route=product/product&path=41_74&product_id=177 or a 6 pin http://tncscooters.com/index.php?route=product/product&path=41_74&product_id=178 throttle. Those links have wiring diagrams. They'll have 24v controllers at either site, but even if the bike is a 24v, go with the 36v. Did it have batteries when you bought it?
Do you have pictures, numbers, ways to identify the motor and controller? If I'm misunderstanding and you want to upgrade to 36v do you already have it? You might be happy merely putting the 36v on the oem motor.