Yes, you shouldn't do this. ;) In this case "Bein" (or in the long form "Gebein") is an outdated term for bone or skeleton.

"Elfenbein" is the modern word for ivory. The meaning of Elf is somewhat similar (though not identical) to English and therefore refers to the perceived beauty of ivory.

A tusk on the other hand is called "Stoßzahn" recognizing it as a tooth ("Zahn").