Use formal, deferential and self effacing terms to show that you are respectful. Instead of saying "ni hao ma?", say, "bo mu, ni hau". My Chinese romanization isn't good. You should ask your girl friend to teach you how. How the meeting and consequences turn out depends on your girl friend teaching you the correct ways to win over the hearts of you potential in-laws.
At the same time, if your girlfriend isn't meticulous or care enough to teach you the customs of her culture in her family, then you know where you stand. It doesn't matter if the family is conservative or not. It's human nature. Since you are of different color, you have to do ten times better than the same skinned to achieve the same result.
Remember the dinner scene in Amy Tan's "Joy Luck Club?" The mother came out of the kitchen bearing a plate of her specialty of steamed crabs. She effacively said, the crabs are not that good. Not tasty at all. So what the gwailo boyfriend did? He said, "No problem." and he poured soya sauce over the crabs! I almost died laughing in that scene. He should have known better. Remember the mother spoke flawless English! I would fault the daughter for not teaching him the proper manners of her culture! It are these little faux pas that cause big problems later. My two cents advice.