OK, first what you should have done was talk to the guy privately immediately after the meeting and told him that you didn't appreciate being talked over and not to ever do that again. As a business analyst, it is your responsibility to translate technical into client business terms and he did not allow you to do your job. His reaction when being confronted privately will tell you a lot about how to handle this in future interactions.
Be prepared to hear something about what you were doing that caused him not to be confident in our client interactions. Take that to heart rather than getting upset, you can't fix a problem that you didn't know existed. But often in these cases, the person is just a dominant person who will walk all over anyone who will let him. So make it clear that you will not let him.
The first step is always to let the person know he or she overstepped and that you are not going to be a pushover who will accept that.
If the person does not have confidence in you, then discuss with your boss what you need to do to fix that idea. One thing that has helped me in the past was to get together with the people in other technical ares before the client meeting and go over what we were going to say so that we presented a united front on the message. In these meetings, make it clear that you want to hear their input and that you may adjust your approach depending on what they tell you.
Now as to telling your boss. If you hadn't let this stew in your mind by not confronting the perpetrator immediately, then you could have handled this in a less stressful way. What you should do in the future is handle it so that your boss knows what you are asking for is support from him or her when this sort of thing happens. Some people will persist until someone higher in the organization confronts them. You want to know your boss has your back when these things happen. And knowing the personalities and office politics involved, your boss is in a better position to give you advice more tailored to the individuals involved. So ask him/her what you should have done differently.
If however, someone gets to you so badly that you need to vent before you can be calm and professional in dealing with it, the proper way to talk to your boss about it, is to warn them that you need to vent and go someplace private. Some bosses are people you can do this with and others are not, so be aware of what type of boss you have. If this is someone who will take you less seriously for getting frustrated and needing to vent, then do your venting outside the office or by writing a email describing everything you are upset about (make sure to leave the To line blank so you can't accidentally send it).
If you do vent, afterwards, think about the actual actions you want your supervisor to take and then bring them up now that you are calmer.
Be aware that there are two possible special cases that may cause issues in a situation like this and you may need to directly address them.
First if there is a male/female or older/younger or racial difference, you may need to address that. Many studies show that women are interrupted more, talked over more, not allowed to speak more, not paid attention to when they do speak, etc. If you are treated as less than because of your gender or age, then you need to be especially careful to be assertive about the matter. I have also seen this happen to people of color or employees who were significantly younger than the person treating them badly.
When I was a young woman, this was far worse in the workplace and I had to grow a thick skin and learn to speak up in the meeting (although perhaps not starting with a client meeting) and not allow anyone to interrupt me. If they try, I interrupt them right back and claim my voice. If people claimed my ideas as their own, I pointed it out; I stood up for others having the same issues.
When people know you will stand up for yourself, they spend less time trying to undermine you. Many women, however, are socialized to not do those things and then the situation tends to get worse instead of better. If you are in this situation, there are some books on communication that you need to read to understand how to better get your idea across. Deborah Tannen has written several goo books on this subject and Talking from 9-5 is a good place to start to become a better communicator. As a business analyst, your job is communication, make sure you learn to do it well.
Another issue is that some developers have a problem with anyone who isn't one. Your boss can tell you if this is a problem here. With a person like this, it is better not to automatically invite them to client meetings, but to get their inputs beforehand instead. Remember, communicating with the client is your primary responsibility not theirs. You should be controlling all interactions with the client and they can't behave, they don't get to play.