There is one formal night on a 3 day cruise and it will be the second night. Many passengers stay on the ship even though it is in port late. Though there are rarely any men in tuxedos and ladies in long dresses, a majority of passengers do dress for the occasion. It is slightly less formal that a longer cruise. Some groups especially the ladies have fun with it. We went one time and all of us had to bring and wear our ugliest bridesmaid dress WITH all of the accessories including stained shoes. One girl didn't have one so she dyed her wedding gown black and wore it. (she was divorced). I do realize that there are a few folks who do not want to dress up. That's fine but please respect those who do. In my 25 plus cruise experience about 90% of the passengers follow the dress code. It is never mandatory except in the main dining room on most ships. Please use the informal dining venue or room service if you do not plan to dress up. As an alternative to formal wear I have seen some passengers wear subtle simple attire such as slacks or a plain but longer dress or skirt for ladies. This is fine and does not detract from the formal atmosphere. Passengers in shorts, jeans and tee shirts who come to the main dining room on a formal night will usually not be allowed in.
Some ships will offer the regular dining room menu for room service and some do not. Check with your cabin steward. For Monarch and Sovereign, I would not recommend room service unless you have a Junior suite or larger as the rooms are VERY small with no place to eat. The casual dining is the best alternative for formal night, or just spend the night out in Nassau. By the time you get back on the ship most people will have already changed their clothes back to normal.