In November 2004, I cruised with the Glenn Miller Orchestra. Radisson Seven Seas (now Regent Seven Seas) usually has a big band theme for their transatlantic cruises in Spring and Fall. In addition to the great entertainment, these are usually two for one cruises.
I searched Ballroom Dancing Cruises, and several different groups were listed. They tend to book blocks of rooms on various ships that we all cruise on including the Queen Mary. So, reservations are made by reserving the date on a specific ship listed. There are also escorts with these groups to provide partners and some instruction. I'm sorry, I don't remember the specific group names, but they shouldn't be hard to find on a search.