Basically what nenjin said, but don't stare too much. Think for example when you are talking to friends and family you don't stare at them with the intensity of a thousand suns all the time, that would be weird right? Same goes when you try to get together with someone. In short, balance is the key.
Also relax, i know you are nervous, she knows it, we all know it, still, try and at least project confidence instead of the jittery nervous wreck that you probably are. To me it seems like women are definitely turned off by that sweaty, nervous guy who looks like he might run for the hills at any second. Instead try to appear calm and confident as if you have done this a thousand times and you are just asking for the check.
Some more double-edged advice:
I don't know how old you are or if you are allowed to drink in your country nor how well you can hold your alcohol. All those play a major factor in what im suggesting here. This is a very selective advice and might do more harm than good.
Personally i have severe problems with talking to people too and alcohol is for me (personally) a life-saver there. But by the gods keep it in check, WAAAY in check. Think no more than two drinks, just enough to get you relaxed. The alcohol helps most people with issues of being too wound up, with the downside that it absolutely screws you over if you overdo it.
There is a reason its called social lubricant, but dude be careful about how much you drink. If you are a lightweight or a nervous drinker, then put in at least two non-alcoholic drinks in between every other drink.
In other words, alcohol can be your friend, but more of that dickhead friend thats just waiting to screw you absolutely over.
But yeah what nenjin said is more helpful in general.