I have a pretty senior position in a large tech company (a director). I have a strong engineering background which is known to everyone I work with. I am respected among my reports, peers and all the way up by everyone. If it is relevant at all, I'm a woman.
One of my co-workers (he is one level above me but I don't report to him), went with me to several important meeting with a 3rd party provider. But any time anyone had a question in my area of expertise (something I personally built, my team built or even highly specialized (and sensitive) area that I am the only one in the room with any qualifications for), he would jump and answer himself based on whatever he knows or think he knows from talking to me or from others. He wouldn't even give me any credit and would just say "we" so everyone we met with clearly understood it as his teams even though he had nothing to do with it.
It wouldn't have bothered me as much because eventually people caught on and started directing the questions to me instead. Except in one meeting where a couple of guys just pointedly ignored any input I had whatsoever. Not in a rude way, just simply looking away after stating any opinion to look at my co-worker and talk to him as if I never said anything, sometimes even crediting ideas I just mentioned to him or to themselves. They even thanked him for work that I did (they didn't know it was me) and he gladly accepted it.
I am honestly extremely upset by this. It's been eating at me for over a week now. I'm also at a loss as to what to do. On one hand, I want to gently talk to my co-worker and express my feeling because I know I will resent him if he doesn't stop his behavior immediately. On the other, this guy may one day become my boss. I don't want to burn any bridges. Part of me really wants to believe he didn't do it intentionally; I think he just thinks he is speaking on behalf of the company. I actually have a pretty good relationship with him otherwise just never really worked closely with him. I think he may be like this with everyone not just me.
What would you do in my place? Also, how should I have handled these guys that completely dismissed anything I said (without being rude outright) for over 2 hours?
Edit: It's worth noting that it's not the first time this co-worker has done something similar with me. I just usually brush it off and wait until he is finished and explain in more detail or provide corrections politely. He seems to accept my corrections just fine and doesn't seem to think much of the whole thing. It got to me this time because it was with people I'm meeting for the first time and that it clearly made some of them dismissive of my opinion just like my co-worker appeared to be doing.