<human>: Can you provide a brief rundown of the text in within 3 sentences?

I've had two 'dates' with a girl the last two weeks, both went really well. We have a lot of chemistry and jokingly teased each other over dinner and some drinks at a bar [for both dates] but nothing physical to show we have interest in one another. Which brings me to this: I'm not too sure if I was blatant enough that these were dates to her or if we were just hanging out which may have confused us both to figure out whether we share mutual interest with one another.

The first outing, I suggested a place to grab drinks, she had to reschedule due to assignments but suggested a restaurant and drinks after. She had a birthday party afterwards which she invited me to come along but I already had other plans. I ended up texting her the next day saying I enjoyed the night and if she wanted to hang out again and we ended up getting dinner and going to a bar this past week.

Again, I failed to show interest in her physically (It takes me awhile to become comfortable to physically show affection). Which makes me think how should I approach a date, a proper date, with her whether we call it a third or our first and for her to explicitly know it's a date?
<bot>: Been out with a girl two times but not sure if we have mutual interest in one another since we didn't call those nights 'dates'. How should I approach her for a proper date?