Which fly or bee bit my wife?

Answer

It looks like a small Earth Bumblebee. Bumblebees can sting but very rarely do so. They are not intrusive and you can basically land them on your hand and put them outside. They are that gentle. If they sting, it is usually when you accidentally push them hard and the animal therefore considers itself in danger. In fact, you will only be stung if you hold something on which or in which there was a bumblebee that you did not see and that is about to crush you.