Well, its different for everybody. My roomate has been with his GF for 6 years, and its really screwed up because not only does everyone like each other despite 2 breakups, but she is best friends with his mom. Screwed up, i know. They basically team up on him, and he's none the wiser.
For me on the other hand, i wasn't dealt with very personable parents. Infact, they are quite the opposite. I will wait as long as possible before i introduce a GF to my mother, or father.
It really depends on the people and the personalities. Some people can just get along with others, while others can't. All of my brothers have learned that their wives should not associate with our mother as much as possible. It doesn't work for my family, but that doesn't mean it can't work for yours
Just...give it your best shot. I would suggest planning an activity based on your initiative, and try to be as personable as possible. If things still don't go ok, well, just tell your GF you gave it your best shot.