[Updated below]
Just a quick correction, I've definitely had bagless vacuums long before the Dyson company was around.
pretty sure you're mistaken. From memory Dyson was unable to get the money together to manufacture vacuums under his own brand, and Hoover et al didn't want him around at all (vacuum cleaner bags are like razor blades), but he was able to licence his design to a Japanese company and also an American one.
There's quite a bit on the internet about the Japanese licenced Dyson - the G-Force - but I can't find anything yet on the American one. It was, I think, sold initially as a carpet shampoo machine, came with a powder you sprinkled on, and then as an industrial upright. I think these were sold in the US for many years before the Dyson brand made it there due to some sort of legal problem
I'll update if I can find the info I'm looking for
[edit: the keyword Google needed was Amway. Read this http://www.amquix.info/amway_dyson.html
In short, Amway entered into negotiations to licence Dyson's design in '84, withdrew after some time then launched their own copy. Lawyers got rich all the way to 1990 when things were resolved and Amway agreed to pay royalties to Dyson. Not mentioned in this article, but I think part of the agreement was Dyson say out of the market for a certain time]