The only option I can see short of high-filler sealing primer and then paint might be to bleach the dye using peroxide bleach similar to what your girlfriend most likely used on her hair before the dye step. Peroxide is a very powerful oxidizer, and will denature most dyes. It's likely to damage the paint, however, so if you rent, you may as well just leave it as is -- it'll cost you the same from your damage deposit when you move out either way.
I suggest you do the following steps:
Anyway, if you are not satisfied with cleaning the wall using powerful chemicals that do not lose paint, you will have to suffer some paint loss. Moreover, paint samples are available in today's market that costs only very less price, you can purchase that and paint the lost portions.
Ask your property manager for a very small quantity of the paint used to paint your apartment. Provide a small jar. They should have it on hand.
Tell him or her what happened and that you would like to repair it with the correct color to preserve your security deposit.
Be sure and thank them.