Do you think my girlfriend will find this one part of my story to be offensive?

Here's the deal: This is a character in a story, right? First of all, friends (or "girlfriend/boyfriend") should be able to say anything to each other, in real life or in a story. In a story, and in real life, people tend to take themselves too seriously, and I think this inhibits creativity. Let go a little bit, free yourselves of all that stuff that is "right" or "wrong" and just go with the ideas...let them flow and see where it leads you! If the character is in a given situation because it makes sense in the story, then by all means, it should stay in the story. I don't see anything at all to be embarrased by.