I will also be interested in the answer to this question, since I have one bought several years ago, and is now peeling very badly. And I am not sure what kind of paint to use. My neighbor painted a concrete one with exterior house paint and I wonder about that too. The birds don't seem to mind!

I would not use bitumen paint. Exterior house paint works on concrete bird baths. It may blister under water though. For a metal birdbath you can use Rustoleaum or latex. Keep in mind that black gets hot in the sun so I would use it either in the shade or in cooler climes. All are safe for birds.