What's helped me when it comes to approaching women was Simple Pickup! If you watch a few of their videos, you'll realize fairly quickly that approaching women, and getting their numbers isn't such a huge issue. I came from the same background. I used to skirt around the idea of even saying hi to a woman. I had to really ease myself into actually being comfortable with interacting with girls.
When I worked at Subway when I got right out of High school, I did one thing that though may not entirely be professional but it did help me alleviate my anxiety and all I did was compliment every woman and even every guy in line on something I liked. And at first I was absolutely terrified at the idea of telling a girl how pretty her hair is or how nice her outfit looked. I was visibly trembling at the idea because I was so convinced that these people wouldn't appreciate what I had to say or what I thought. Eventually I weaned myself into starting an actual conversation with women and I tried this at a local mall of mine, and I will say the ways that I approached women were absolutely cringe worthy and thankfully the way I approach girls now isn't so bad.
Here's a list of my favorite and what I feel to be the most helpful/motivating videos from Simple Pickup!
It's taken me a considerable amount of time, but I've gone from shaking in my boots from just saying hi to a girl to proactively engaging with women, getting numbers, being friendly/playful. One thing I do is I ask a girl out on the spot after talking to her for a short time, and this way I can screen out women whom aren't interested in me, but for you, I would focus on more basic things before you start getting numbers and asking girls out. I'll reiterate this again and the best thing for you to get comfortable with approaching women is saying "hi, having a great day?" to every girl you pass by and then start complimenting them on their hair, eyes, clothes, general appearance. After saying hi and complimenting them has gotten boring, find a girl that looks like she's waiting for someone, sitting by herself, standing by her self and strike a conversation with her. Don't approach girls that look like they need to be somewhere.