Movie dates give off a weird vibe. Like when you think about it by pretty much any metric you pick it's not a great idea. The only reason people do it i because cultural tropes have taught them that's what a date is, which is also the problem here.

The central issue here from what I can put together is you've asked her on a "date date", which feels like a bit much to most people. Like if I met a girl and chatted to her then she asked me to go see a movie I'd be apprehensive myself for that reason. THen even when you pulled back it felt a bit serious, which is just the opposite side of the same coin.

The rule here to bear in mind is nothing's a big deal. Pulling back a little's better than doubling down, but again, it all feels kind of serious. Your aim is to be in a state of mind where hanging out with a girl isn't some big thing, and if a girl doesn't want to meet then cool, you've got your own stuff happening and you'll catch her at some point.

Ease up on it for a few days, pick something you actually want to do, but preferably something where you two can interact instead of starting at a screen. Message her and ask her how she's doing then go "ah, there's this thing/place I wanna go to, fancy coming along?". If she says yes cool, if not, no big deal. Simple.