My Lily is a white long hair too, Marelli , but as she refuses to go out, her chances of getting dirty are pretty slim. However her tail sometimes looks as if she is a bottle blonde with dark roots. About twice a year I clear the draining board, fill the sink with warm water, then sneak up on her while she's asleep. With Mr P's help she is plonked on the draining board, her tail is dunked then lathered up with John Frieda "Born Blonde" shampoo and rinsed.
If timed right, the whole exercise can be completed before she realises what's happening, but then she does always take quite a bit of time to wake up, and is also exceedingly thick.