In the beginning of Twilight, Bella swan explains that it is Mid term during spring at Forks High School. If that's the case, when does the TERM start at Forks High School?

America schools have 4 semesters during a school year...first two start (usually) in Sept and go thru the end of Dec...with the last two starting Jan thru the end of May....

That particular term probably started after the Christmas holidays, and it was early spring during mid-term.