For those who use English measurements, the distance is around 675 miles, or about the distance from Boston, Massachusetts to Quebec. So it's an 11 hour bus ride, maybe more. That's kind of uncomfortable even in good buses, but hey, it's your butt.
Your parents are probably concerned about other things. What will your brother do during this vacation? Where will you stay? Where will he stay? What will either of you do for food? Five days is a long time to impose on this girl's parents, particularly because there are two of you doing the imposing.
And that doesn't even get into your relationship or whether you will sleep together while on the road, etc.
Yes, you are 18 years old, but try to see at least some of this from your parents' perspective, and from your girlfriend's parents' perspective. You are expecting them to feed and house two more or less stranger teenaged boys for nearly a week. Do you have any idea how costly that is?