The master of ceremonies was an official position in fashionable towns like Bath. Their job was to oversee the balls and parties. Their duties spanned from enforcing the rules and keeping the peace to making sure everybody was dressed correctly. As we see in this line, one of their most important jobs was to introduce young men and women (Austenonly, "The Master of Ceremonies: The Georgian Assembly Room, Part Four", https://austenonly.com/2013/02/28/the-master-of-ceremonies-the-georgian-assembly-room-part-four/ ).

In response to the French Revolution, by the late 18th century, constricting, formal styles of dress, reminiscent of French aristocracy went out of fashion. Instead, looser styles of dress, inspired by classical Greek and Roman fashions, rose in popularity. Lightweight, sheerer materials, such as muslin were popular, as was an empire style waistline ("Lord Scott", An Introduction to Ladies' Fashions of the Regency Era, http://www.wemakehistory.com/Fashion/Regency/RegencyLadies/RegencyLadies.htm ).

The word "address" in this context is different from the modern definition of a place of residency. In this context, "address" refers to a "manner of addressing another" (Johnson).

"A state of intense delight or euphoria" (OED).

During this period in England, men and women could not interact, much less dance together, unless they were formally introduced by somebody that they were both acquainted with (Maria Grace, The High Stakes of Etiquette for Young Ladies in the Regency, https://kimrendfeld.wordpress.com/2013/04/29/the-high-stakes-of-etiquette-for-young-ladies-in-the-regency/ ).