I got attacked by several bees before too.
I was walking my dogs though a golf course that is near my house. Is was a beautiful day and there was not a single person around.
I went to visit a bees hive that is in a tree that is just off of a path. I have been visiting them for several years now and have watched them thrive.
This particular time I went over to have a look to see how they where getting on and it didn't take long for them to start flying towards me.
Just like you, it started with one bee landing on me and I was just going to ignore it but then I saw it started to wiggle its bottom and I knew it was about to sting me.
Not wanting to get stung, and not wanting for the bee to die, I brushed it off and started to move back. Even though I wasn't even that close. More bees started to fly towards me and that's when I started running.
I ran with the dogs, making sure that they don't get stung but the bees quickly caught up with me and some started to land on my left shoulder and started to sting. There was about 3 on my arm and some on my neck and head. I too was " litterally fligging my arms around in the air and shaking my head in terror". It was quite scary but I managed to get away with only several stings on my arm. They didn't even hurt that much so I don't think that they stung me properly before I wiped them off.
I still visit the bees and they are doing well. I have never had a problem with them since. PS. The dogs are also fine, none got stung.