Wow! Moxie. My Papa used to capture a swarm like this and take it home to a bee box with a female and have a new hive. This is the easiest way to start one. Sometimes he was called to take these from folk like you that had them in their yards or from folks in buildings with them in the attic or even once in the walls of a church behind the pipe organ. That was one of the biggest jobs he ever did. He had built up an immunity to the stings but still wore protection when he had a big job. Take care and keep any vibration away until they move on. It is the vibration of the mower and your disturbing the bush that riled them up.