In the bee world, bumblebees are really big. A large queen bumblebee of a relatively large species, like Britain's Buff-tailed Bumblebee (Bombus terrestris) may be up to 22 mm (a little less than an inch) long. Compare that to one of the tiniest bees, the solitary bee, Quasihesma, from Australia, less than 2 mm (around 1/16 inch) in length. This tiny bee could easily sit on the head of a pin.
But bumblebees are by no means the largest bee. In North America, the common Large Carpenter Bee (Xylocopa virginiana) is still larger on average, with a maximum length of 23 mm (just under an inch). These carpenter bees look a lot like bumblebees, and I often have to look carefully to see the metallic-blue, shiny abdomen that distinguishes this species from the furry abdomen of bumblebees.
If you are bee watching in the jungles of Indonesia, you may see the rare Giant Resin-bee, (Megachile pluto), a full 39 mm in length (about an inch and a half). So the largest bee is about 20 times larger than the smallest one, with bumblebees coming out somewhere in the middle.
A large bumblebee queen has to be big, because to keep order in the colony she may have to be tough. Her worker daughters are not always the meek handmaidens to the throne that their station demands. Some of the larger workers may try to take over egg laying, although their eggs can only produce males. Then the queen will have to bully them back to their normal duties.
Bumblebee queens may keep their workers under control, but they don't win all battles in the nest. Cuckoo bumblebee females tend to be stronger and more heavily armored than the queens of colonies they parasitise. When the cuckoo enters the nest a violent fight with the queen ensues. Usually the cuckoo female is the winner and the queen dies.
Size is relative, and bigger isn't better, just different. Big bees are large simply because that size suits them to whatever role they play in the environment.