We sprayed several colors at my old job... I don't recall ever doing white, though. I've seen red fade to nasty pink... But I really think it depends on what they use to tint the bedliner. I did some Googling and ran across this:
"Some LINE-X dealers, including myself, use Dupont Ful-Thane Nason for color matches, including white. Nason is a urethane based automotive paint, it will not fade. I don't recommend white bedliners unless you put on a tonneau. The white textured bedliner shows EVERY spec of dirt and it's not easy to keep clean. For flare/rockers, I'm 50/50. BTW, you'll pay a premium for white, it's harder to work with. "
http://www.turbodieselregister.com/threads/142185-White-bedliner
As far as keeping it clean, I always just used purple power on mine. Sprayed it on, maybe take a big brush to it or pressure wash it if it was really bad, rinse it off. Over 9 years it always looked brand new after I cleaned it, granted it was black.