I personally like quiet girls but Im a quiet guy myself so I have to get out of my comfort zone and talk a lot to get a quiet girlfriend. Thats the only way how introverted person can meet other introverted person - by becoming extrovert for a moment.
I talked with a work colleague who is quite talkative guy and he said most important thing for him is that girl is not a complete loser in terms of being strong person.
If you are quite shy with guys but if you would find a guy you like then you could ask for her phone number or FB account and express yourself better with messages until you would be ready to take that jump and meet that guy for a date or something like that.
Doubt kills more dreams than failure ever will