I decided for the example to go from black hair to blonde, not because it's a good idea, but just to show that it can work on some level.

First thing I did was I took the hair's image map and plugged it into a bias and gain node.  These nodes strip out the unwanted color and give me a little control over the final look of the hair.  If you notice in the picture some of the details are lost around the roots... this is why I think black makes for a good example: it loses some information at the top (better to go from light to dark or medium up or down) because of how dark the image was.  Again, this example was just to show the concept.  After that I plugged the math functions into a blender node to combine their effects and finally a simple color node (in this case yellow to produce a blonde look).

It's not perfect and the roots are still a big problem, but you can see it doesn't look too bad either.