Going to his house for the first time

I met this guy on Bumble a month ago and we’ve been talking pretty consistently ever since. We went on two dates, the first one to a restaurant for lunch and the second one to the zoo, and both of them were really great! We haven’t broken the physical touch barrier yet other than a quick hug at the end of our first date. I get really shy around him and forget to ask him questions so I feel like I still don’t know that much about him. He always asks about my day and if I’m feeling well over text, and from his behavior on our dates, he seems very sweet and respectful.

He invited me to his house tomorrow to watch Batman because it’s one of his favorite movies and I’ve never seen it. I’m just scared because I don’t want to do anything sexual yet and I’m not sure if that’s what he’s expecting after watching the movie. I do really want to kiss him though. Going based off my current perception of him, it seems like he’d respect my decision even if he was expecting to have sex. But idk I’m just anxious bc this is my first time ever dating someone and this is all new to me 😭 Any advice? Also for reference we’re both in college, he’s 21 and I’m 22

UPDATE: I ended up feeling comfortable enough to go and was very cautious, but there was nothing to worry about! We just watched the movie and talked a bit and our arms touched a little. Lowkey think we’re both scared of making the first move lol which is what I was thinking from our last date. But I had a good time, and we’re already planning to hang out again in three days. Thanks for all the advice :)