In the Sisterhood of the Traveling Pants series by Ann Brashares, one of the main characters is named Bridget Vreeland, but her friends sometimes call her Bee.
Buzz Buzz Buzzzzzzzz. I perfer the spelling Bea. Either way though, nobody's gunna miss the connection with the animal, but Bea just looks right. Though it makes sense to choose this variant if you're more concerned with people pronouncing it right, and not saying "Bee-ah".
Bees sting! Why would you want to give this as a legal name for your daughter? However, it's fine if it's a nickname for Beatrice or anything else starting with B.
I have a friend, who has told me her name a million times. I don't know how to pronounce or spell it so I have her Bee because it starts with a B. She loves it.