"The trip will be over in June."
Translation:Seyahat haziranda bitecek.
bitmek is intransitive (it has no object) so you use it when the subject is something that ends "by itself".
bitirmek is transitive (it takes an object) so you use it when the subject causes something to end.
For example, Öğretmen ders bitiriyor. Ders bitiyor. "The teacher ends the lesson. The lesson ends."
Rule of thumb: if you can replace "end" with "cause(s) to end" or "makes end", then you have bitirmek. "The teacher causes the lesson to end. / The teacher makes the lesson end." -- works. "The lesson causes to end. / The lesson makes end." -- makes no sense.