Sometimes when you're talking to a woman you've recently (or not so recently) met, people will interrupt you.
This isn't always unavoidable; there are things you can do to reduce how often it happens.
For one, often if you ignore people attempting to butt into your conversation, and your conversation partner does as well, the interrupter will begin to feel awkward, then leave. So, don't break circle.
For another, use some situational awareness: don't approach women someone's likely to interrupt you with during the first three minutes of conversation.
For a third, you can use a little group theory to get a woman's friends (if she's with friends) on your side.
These three things in concert will dramatically reduce the number of interruptions you'll deal with.
Nevertheless, no matter what you do, you are still going to encounter interruptions from time to time.
It is simply a part of socializing. Sometimes the people you're talking to have other people who want to talk to them too (and who won't be content to wait idly by until you've wrapped your conversation!).
How you deal with this, and how you recover, can make all the difference in the future of your interaction with a girl.