Cleaning white laces?

They're stained blue because of the colour rubbing off the shoes. Any tips on how to clean them? I've tried the bleach & water in a bottle technique but it didn't do much.

Or should I just buy new ones? Thing is I wear the shoes quite a lot so the laces get dirty a lot so I'd rather find out if I can just clean em instead of having to buy new laces on a regular.