Those little stubby antennae are your first clue that this is not a bee, but rather a benign (read: stingless, biteless) hover fly. Not that bees aren’t very benign (they are for the most part!), but people often confuse these flies for bees. Which of course is the point, my tricksy hobbitses.
I was really tempted to call this (outright) a “drone fly” but I’m not sure that it is generic enough of a term to use, and I couldn’t find Eristalis sp. that particularly resembled it, so for the taxonomically-inclined file another one under “frustrated.” (Black and white version after the break.)