In flight, it looked like a bee and sounded like a bee. At rest, or perhaps sunbathing, it looked to the naked eye like a bee with something sticking to it.
With the magnification of a photo, the “something sticking to it” proved to be a single pair of wings sticking out from the body, when resting bees’ wings are folded back along the abdomen. So it’s a fly; specifically a dark-edged bee fly (Bombylius major)