Whenever possible, get a real person to introduce you
The best way to lower her inhibitions about talking to a stranger is to get a mutual friend to introduce the two of you (then you're not a stranger!). If you're cruising your Twitter or Facebook feed and you see some random cutie in a photo with one of your boys, don't immediately send her a friend request or a random message. As discussed, a compliment as an introduction is an always-fail approach, and "Hey, how are you? I don't know you but...you seem cool" isn't much better. What are you basing this on? The three small tidbits of info about her that Facebook hasn't blocked? Sure, it's nice to think that we seem that intriguing based on the single sentence bio Twitter allows, but it's just not possible.
Ask your mutual friend to find out if she's single and possibly set you up with her, even if it's just a casual group meeting at a local bar. If your mutual friend thinks highly enough of you to vouch for you (and reach out on your behalf), you've nullified any potential creepiness; in fact, you've actually won a few points.