I recognize myself in this. Sometimes I'm very introvert, have nothing to say (and couldn't care less about it) and find it hard to keep a conversation going. I'm out of state, for short. Other times I'm extrovert, extremely social, outgoing and funny. In state. Here is how I have learned to deal with this.
1. Learn
conversational techniques. Be aware of so called
hooks in the convo. These are things the girl mention but don't elaborate on. For instance, she says "yesterday I went to the mall with my friend". Some hooks here are "who is this friend?" and "what did you do at the mall?".
2. See it as a long term project to gain and maintain your
social momentum. Keep talking to people all day long, all week long. As you do this you will notice how it becomes easier and easier to open sets and talk in general. Also notice how this momentum spills over to the next day, which means that one day's hard work pays off.
3. Release all pressure and performance anxciety you may have on yourself. Beautiful girls can be really boring, not contributing to the conversation at all (usually due to lack of skills), or just babbling about stuff you can't relate to. If you meet a boring girl, ask yourself why you even bother. Ditch her if she doesn't thrill you. Girls need to learn game too IMO. Being able to do this is key to get the right attitude in your game.
4. If you run out of things to say despite all the above, try to be present in the moment, mindful, and comment on things you see and hear. It can be fun to have a child's enthusiasm about things, like "look! and ice cream bar! I love ice cream, let's have some!", running towards it holding her hand.
5. Be self amused. Don't try to please the girl. Please yourself.
I hope this helps.