You should be able to cover it with almost anything. Maybe there's a plastic-like thing that you can use instead? Or perhaps a towel that you don't mind getting stains on?
Some people don't cover it at all, it depends on what shade of color you're going for.
The best thing is to google henna to find forums and such, I've found that there are a LOT of people dedicated to using henna and I'm sure that they'll love to give you advice on different methods
