Personally, I would go with your complete boyfriend answer.... "no, I have a girlfriend". That is a polite way to put it, and you're not out there flaunting it around, you're just answering a question.
I came out at work in a similar way. And my co-workers were fine with it. Got a couple funny looks, but other than that, everything was fine.
I, like you, don't have little gay parades for myself. I'm not one to be all out there in peoples faces about anything, much less my lifestyle. But it is good for people to know. Like Northernbird said, there could be dinners or family times at work, and you want to be able to bring your partner with you.
Keep us informed on how it goes, I'll check back in on you.
Joanie