Can you bring a bicycle into the US from china?

Sure.

I it's only one, for personal use, and you bought it while staying there, there's no trouble with customs - so you'll just have to figure out how to get it shipped.

Easiest is probably to visit a few bicycle stores, try to get hold of one of the cardboard boxes that bikes gets delivered in. Tuck your bike in there, add as much bubble wrap and stuff as you can manage. Then bring the bike to the airport with you. Expect to pay about 100 USD for the extra piece of oversized luggage.

Otherwise you'll have to use a courier, UPS, DHL, TNT or similar. Expect to pay more.