"Bilbo" is an English catch-all word used to very generally refer to the Spanish "Utilitarian" cup-hilt swords, so often found all over America. They usually had a wide, relatively short sturdy and well tempered blades, very practical and comparatively unadorned. The grip was more often than not wood, sometimes covered with wire.
Bilbos are tough, flexible, and unadorned. Are those qualities applicable to Bilbo Baggins? His journey in The Hobbit certainly tempered him and he demonstrated great flexibility as he adapted his skills to myriad situations, including a battle of riddles, slaying giant spiders, smuggling his companions out of an elven dungeon, and stealing from a dragon. It's also not much of a stretch to describe the earthy, practical hobbits as unadorned. There is no evidence that Tolkien derived the name for Bilbo Baggins from the sword. More likely, he derived the name comes from Old English sources. However, it's hard to believe Tolkien--the philologist and contributor to the Oxford English Dictionary--didn't know about the word bilbo.