You seem like a decent enough bloke so I'll take you under my cool and confident wing for a moment.
First things first: STOP PEDESTALIZING her. She will smell this a mile--yes, full mile--away. She's just another fellow human being.
I generally will not 'cold approach'. I suggest that you not approach unless and until you receive choosing signals. And when you do, ACT! Right then. On the spot.
When you do, and you better or we will all take you to the woodshed over this, you need to remind yourself to not put her above you. I don't care if you have to keep repeating to yourself, "Do not pedestalize her... Do not pedestalize her..."
Keep this simple. "Hi, there. How's it going?" Give your name and get hers. If you absolutely need a scripted ice breaker just mention that you've noticed her around and that she's on the softball team. Segue from there. BRIEFLY segue from there.
Finally, and here is where personal preference admittedly comes in and there are those who would suggest against this, you GIVE HER YOUR #. Have a pen handy and something to write on. Just tear off a sliver of paper and write it down. As you're doing this, simply say, "Hit me up if you'd like to grab a coffee sometime."
You do this ONLY if you like how the convo went. If you don't like how it went you do not offer your #. You just tell her to have a good one and move on. Point being, this is all your call. You're calling the shots on this. You're deciding to reject her or not by deciding to offer your # or not. You're not asking her for anything, regardless.
Guess what? Pressure is off you. If, and only if, you like her, ball is in her court. You've initiated the dance. You've put her in a position to chase you. You've presented yourself as a potentially receptive challenge.
If she's interested, she will contact you. If she doesn't, for any number of reasons, let her be the one to kick and second guess herself. Either way, you continue to navigate your way through life being the fly cat that you are.
Got it?