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.
"Carpe diem quam minimum credula postero"
Seven Seas Explorer - Miami - Venice - Mar 2017
Silverseas Explorer - Arctic - Aug 2017
Seven Seas Voyager - Rome to Beijing - Oct 2017
Seven Seas Mariner - Lima to Buenos Aires - Jan 2018
Silverseas Explorer - Siberia - Jul 2018
Seven Seas Mariner - Australia Circumnavigation - Dec 2018
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.