I made contact through the Natural Beekeeping forum with someone who had a bumble bee nest in a bird nest box. He also has a one-year-old daughter who has mistaken bumble bees for spiders and tried to pick them up. He was adamant (understandably) that the bees had to go!
I explained that the bumbles had probably been attracted to the box as he had "given the birds a start with a nest" by adding some dog hair to the box. Bumbles love fur in their nest!
I offered to remove them on the condition that I could take them in the nest box, as removal from the box would be virtually impossible!
The nest box had been there for some time and attaching screws were rusty, so the box was sawn from it's supporting post. The nest box was placed in a fabric bag and driven home. The new site was decided upon and the box attached.
The next morning the bees were flying happily having exhibited a similar orientation flight to honey bees, but a few days later there were none to be seen.
I've no idea what they were up to, but a week later I was looking at the box, wondering if I should take it back down and clean it out, when three bees "buzzed" me on their way back into the box. That made the bee guardian very happy! They have since been flying every day between the rain drizzle and obviously more willing to fly in worse conditions than honey bees!