Altough both sentences mean the same, as in English, in Spanish we have many ways to say the things we want to say. Both sentences have accurate translations and both are right to say the exactly same thing.
'I am going to introduce you to my girlfriend' is for
"(Yo) Voy a presentarte a mi enamorada"
'I am going to introduce my girlfriend to you' is for
(Yo) te voy a presentar a mi enamorada.
Because in the first one you are saying that your girlfriend is the one that is going to know your friend, and in the second one you're saying that your friend is the one that is going to meet the girlfriend. As I said at the begining both mean the same but is just the form that you're saying it. Probably your girlfriend woul like to say that you're introducing the friend to her and not the other way, ha ha ha (at least mine would want that).
Another thing I would like to say is that the word
novia actually means fiancèe or bride, not girlfriend, but it depends on the region, I know that in Argentina they usually says
novias when they're talking about girlfriends. But, for example, here in Perú we call for
enamorada, though it is not that accurate because it is not ascertainable that the girl you hang out with really loves you as the word suggest, but I think there's no translation for the word
girlfriend, I think the ancient Spanish, who invented the words where more "love-believers" than English ones, just saying...