Should I pursue a relationship through parties, or should I try to get a date?

At my work there's a woman (22) who I (24) like, who has been working there for a couple of years. She is beautiful and fun, as far as I know her anyway.
This whole situation started when I told one of my friends about her, saying that I thought she was really attractive. My friend then proceeded to quite clumsily ask his sister (her best friend, small town) about this woman, and he also told her what I had said.

My annoyance at my friend was tempered by the fact that the sister had said that the woman liked me as well, going so far as to look up when I worked and so forth.
The sister and the woman has since then been pushing on and off for us to go to the same parties, to test the waters.
I have agreed to this, with little to show for it.
As anyone who has ever gone to a party, they know that it's not that easy to get one on one time with someone. People are drunk, it's crowded and there is blaring music all the time.

Just a few days ago, there was a Christmas party of sorts, one of the biggest parties of the year.
I knew she was going to be there, so I prepared extra, everything from my clothes to the energy was on point. Unfortunately, but not really surprising, circumstances made it so we barely got to say hi to each other. She had to follow a friend home, who had forgotten her license, bad luck basically.

As I was walking home alone and disappointed, in the rain (dramatic, I know) I thought to myself that why can't we just go on a date? I've gotten the feeling that she wanted to meet at parties where there are more people, less awkward, less pressure, would be my guess, this might just be my imagination however.

TL DR: My question is this, should I keep waiting for one of those parties that come around every few months and hope for the best, getting to know a girl, or should I just ask her out on a date, and hope it doesn't scare her off, I dunno?

If you've read this far, I thank you and I'll apologize for any errors, English is not my first language.
Should I pursue a relationship through parties, or should I try to get a date?
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