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Probably because the Little Sister has been reconditioned to give him the aforementioned affectionate name.

The Little Sisters call their Big Daddies "Mr. B" because they are brainwashed to trust the Big Daddies completely, and they call them by loving nick-names. "Mr. B" is also a shortened version of "Mr. Bubbles", which is how the little girls think of the Bouncer Big Daddies because their helmets are almost bubble shaped. The reason might also be that the diving suits the Big Daddies wear produce air bubbles when underwater.