The students may be whining in their hearts, thinking that I nag too much and that I am such a spoilsport to lecture them to behave themselves before they can eat.
Someone who isn't interested in doing fun things, especially someone who wants to do everything properly, that doesn't want to break any of the rules, that's what a spoilsport is.
Here what Bethany means is that she would rather have the reputation for being a spoilsport than being the kind of person who keeps drinking as the night goes on – at least, I think that's what she means.