Since you are drilling into two quite different materials, this might be a difficult problem. Personally, I would try on a discarded bathtub a few times before going for the real one. As for how you should drill, I would suspect that you need to do it in several steps. Since bathtubs usually have quite thick metal, it might be difficult with a punch. Drill as large as possible with a good drill from the back side and then sand the edges with a rotary sander like a Dremel. It will take some time as you can't use rough tools because that might crack the enamel. I just realized while writing this that it might be possible to "cut" through the enamel with a Dremel and then be able to drill more "recklessly".
