1. Navigate to: "C:\Users\[YOUR USERNAME]\AppData\Roaming\Bioshock"
2. Open "User.ini"
3. Find "NumPad0="(you can use a different key if you want)
4. Add "ToggleHud"(without quotation marks) to the end of it. It should look like this: "NumPad0=ToggleHud" (You can also experiment with ShowHud, and HideHud).
5. Save and under the file properties check "Read Only"
Now, when in game, just press the 0 on your numberpad and the Hud should disappear/reappear.
This is how to do it in Windows 7. The directory you need to find may be different depending on your OS. Try doing a file search for the User.ini file on your C: drive.