I taught twelfth grade in a small bais yaakov high school for over twenty years, and I never encountered a class that did not become weepy and nostalgic by the time the year drew to a close. Unless there are some serious, underlying issues with your class, this will happen to yours as well!!
There are so many opportunities for collaborative activities in twelfth grade–yearbook, senior trip, concert, chaggiga (and whatever else is relevant in your particular school)–that naturally, you are going to bond by the end of the year. Some practical suggestions: individual or monthly class birthday parties? “forced” interaction around the yomim tovim with random pairs but in which everyone participates regarding some activity (candygrams for Rosh Hashana, mishloach manos, etc.)?
B’Hatzlacha!