Introvert here. I met my now introvert wife at speed dating.

If you haven't done it before, you are in a room (usually a rented out restaurant so its just for this event) with lots of tables. At each table is a woman. As a man, you are directed to sit at a specific numbered table where there is a woman seated (all the other men do the same to the individual table they are directed to). A bell rings. You have 5 minutes to talk to each other and learn as much as you can about each other. After 5 minutes, the bell rings, and the woman stay seated, and the man moves to the next higher numbered table. You have a card with the woman's name on it and you should REALLY make notes, because you won't remember which things you thought with each person. The women do the same with their cards.

In under 2 hours each person now talked to 14-18 potential mates. At the end of the night you go online and mark which of the women you're interested in hearing more from. If any of the women you mark also mark you on their side, you're given an in-app communications channel and you can choose to share personal contact information from there.

When you're sitting at the table talking with a woman sometimes it seems like that bell rings as soon as you sit down and you wish you had more time. Those are the ones you mark on your card to talk more with. Sometimes, you're 1 minute in and you're dreading waiting though the next 4 min. Those you do not mark.

I'd recommend you give Speed Dating a try.