Bilbo is an actual word separate from Tolkien's name for the hobbit, that's why. Look it up, it's apparently 1. A device for punishment. See bilboes. 2. (historical) A kind of sword with well-tempered and flexible blade, originally produced in Bilbao.

ETA: Actually, I wouldn't be surprised if Tolkien knew the second definition and used it on purpose, he was a philologist after all.