Okay – this should work. Go to Sephora and buy two Bliss waxing kits. Then go home, you take one and give the other one to your girlfriend.
Then give yourself a bikini wax. Most women cannot give themselves a bikini wax because the thought of inflicting that pain on yourself is just too much to bare, so I have a feeling she won't be able to go through with it. If you however can, you win.
The hair will grow back so no harm done. I dare you to do it.