How do I nicely ask her to dye her hair without offending her?

If you find out her reason for quitting dying her hair, you'll have a better basis for framing your request. If she didn't think it mattered to anyone, you can correct that impression. If she thought it was too much trouble or made her hair too fragile, then you have to be much more careful, if you broach it at all. And asking the question will alert her enough to your interest that if she's open to dying again, she will try it or ask you more about what you want. Otherwise, you should just wait until it comes up.