I think it depends on the situation. If you’re out at a bar or at a party, you need to be able to call attention to yourself in some way in order for someone there to notice you. There’s a lot going on in situations like that, and people who are too afraid or nervous to have fun or talk with someone sort of get lost in the shuffle. Extroverted girls are much better at this and are therefore more likely to gain the attention of a guy.
If you’re in a much smaller, quieter setting, however, then being introverted and shy might help you – he could find you mysterious and would want to talk to you more to find out what you’re all about, or he could find it endearing. In situations like this, an overly extroverted girl who is loud, boisterous, obnoxious and disruptive would most likely grate on everyone’s nerves (although some guys still might like this, you never know), and people would take more notice of you – the girl who is reserved, definitely not annoying, and has some obvious inner-peace. So I suppose my advice would be to somehow get the guy you are interested in in a situation like this, where he is able to really notice you and is not distracted by the crazy chick doing keg stands.