The human mind comes up with its own defenses to protect itself from unpleasant feelings. Do not look at being shy as a handicap. In order to get over it you first need to accept it and approach it with the right attitude.
Know yourself. Find out and put a tab on the root-cause of your shyness, and address it directly, instead of beating about the bush!
Though you may not want to be with someone who wants to be with you just because you also like Pink Floyd, preferences do matter. They give you things to talk about! But that doesn't mean you should alter your preferences to be with someone.
If a girl compliments you, you can respond with something like "Thank you, I am still learning", or "Oh I still have a long way to go" but do not respond to every compliment with that. It may make you seem like someone with very little self-respect and self-esteem.
One of the ways to get a girl interested in you is with a good conversation, better still get them to start talking. So do away with being awkward, and start talking!
Besides, she is going to love that you really want to get to know her as a person, and you aren't an 'all-me' kind of a guy. You are sure going to earn yourself some brownie points here!
If you are talking about something you both do not agree upon, make your point and support it with reasons. Women love men who think, not those that have just blind preferences.
You may not be someone who cares much for his looks, but girls love well-dressed and well-groomed guys! That does not mean you go overboard and turn up for coffee in a trouser and shirt! Dress according to the venue and occasion.
Keep these tips in mind, and you will soon find yourself easing out into the meeting and enjoying yourself. Once you get started, you are bound to find your own ways to overcome your shyness. Best of luck buddy!