Bris - ברית - means covenant or agreement.
When we say we are "going to a Bris" we are speaking in American-ish, but we are not using the term correctly.
Whether we mean to say we are going to a circumcision (which is technically true), what we really mean is that "we are going to a Bris Milah Ceremony, a ceremony in which the Covenant made over Circumcision will be reenacted and reaffirmed."
Of course no one wants to say that, so we just say we are "going to a Bris."
But just as you can't go to a covenant, you can't go to a Bris.
You will be attending a Milah (circumcision) that affirms the Bris.
What is being affirmed is the Bris Milah - the covenant over circumcision.
Having said all that... see you at the Bris! (Now at least you know what I mean!)