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Bumble Bees are really very benign, they hardly ever sting anyone unless actually physically abused. Generally when a nest is disturbed, a number will come out and fly around making quite a noise, however it's all show. They can sound pretty terrifying, though.
They will dissappear naturally in the Autumn as only the queens survive the winter and they do so in hibernation. There are always quite a few nests around and removing the ones you have will only have a modest affect on the number of bees active around your garden. In my very informal counting of natural nests I see in and around my own garden, I suspect around 10/15 colonies an acre is common (50 per hectare?). Bumble Bees don't swarm like honeybees -- you'll not see thousands of them. They don't do any damage.
If you can try to live with them (only until the autumn), you'll see how harmless they are and may learn a lot about them. Sit quietly near the nest and watch them toing and froing. They may come and have a look at you as they will be a bit surprised at the new addition to their scenery, but they'll very quickly get back to work.
They have a fairly hard life and can't afford to worry about much more than surviving and raising their young. In spring, the queen comes out of hibernation and finds a nest site. Most nest in old small animal burrows -- mouse, vole or shrew holes, a few on the surface of the ground. She will build a nest of fluff or moss and make a tiny cup of wax into which she'll store enough nectar for a few days. She will make a single small structure from a soft wax into which she will put some nectar-soaked pollen and and a few eggs. She will then curl up around those eggs and incubate them, only leaving them for very short periods to feed from the nectar pot. When those bees become adult they help around the nest, the first few are always too small to fly, so the queen has to do this again a few times until there are enough workers to permanently incubate the new bees so that they grow strong enough to forage on the queen's behalf. Then the queen can at last rest and get on with raising new queens for the coming year. Few colonies get beyond a couple or three hundred individuals. Sadly, most colonies will fail and die.
Things you could do to make it easier to live with them are to `fence' the area from intrusion -- just something to remind people or pets to give them a little space. Maybe a couple of square metres becomes wildflower garden for a while. If you have very young children, perhaps the fence should keep the children out. With children of about 5-years or older, you can probably get them to watch the bees and understand not to try and catch them or squash them. Even then, they rarely sting.
The stings aren't so bad anyway. Both my wife Sue and I _have_ been stung, in my case after 40 minutes spent digging out a particularly deep nest that did have to go (the pre-mixed concrete was expected first thing the following morning). In Sue's case, she regularly catches them indoors and puts them outside, just by picking them up inside a closed hand. One only, ever, has stung her "like a tiny electric shock".
The red-tailed bees (probably Bombus Lapidarius) right under the shed door are a little tricky because they'll get confused when the door is open and because steping right over their nest might disturb them. All bees learn where their home it to a high accuracy, but if you can put a long narrow board to one side and slide it across a little each day, they should eventually end up using the relocated entrance round the end of the board. You can push from the far end to ease your nerves.
The large ones (with white tails?) under the tree stump are probably Bombus Terestris. The queens are huge -- an inch (25mm) long or more and very fat. Workers are always smaller.
If you find you really can't live with them, it's unlikely they could be rescued. Digging up tree stumps without damaging nests is almost impossible and unless we can move or lift the shed there's little we could do there either. Your local council may be prepared to kill them, and there are pest control companies that will. You could also dust the hole with a proprietry crawling insect killer. But please try first to give them a chance -- they're our friends and vital pollinators.
Gordon