I like this girl and afraid to ask her out?

A few weeks ago on the night before Halloween one of my good friends invited me to a Halloween party at her apartment. I dressed up as three hole punch Jim from The Office lol, and I met this girl who I thought was very cute. She and I talked for almost 45 minutes. Even my friend thought she and I hit it off. I think she has a little bit of social anxiety because the last time I saw her she didn't stay out for too long and had to leave (perhaps she's introverted?) Get this, she's never seen the movie Alien. But anyway im seeing her again Saturday night with my same friend and I'd like to ask her for coffee or spend time with her in her town. Nothing fancy just a little hangout. Now before you reply saying "you're going into the friend-zone. Dont", that's where I tend to overthink. I want to ask her for coffee which is what my instinct tells me, but I don't know whether or not I should start as friends or if we do have coffee together, will she think its not a date? My friend and her boyfriend started off as friends and now they're together. wtf. Ugh I just dont know. If it happens when you least expect it, whats the point of being romantically interested in someone in the first place? Do I have to suppress my interest or something? How do I let things happen naturally? I need Tylenol.

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Update: so last week I actually was able to muster up the courage and ask her to coffee. It was kind of a mixed reaction and she replied with "ill have to see". So I have no idea whether or not thats considered rejection
I like this girl and afraid to ask her out?
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