Personally I wouldn't be able to initiate a conversation like that - way too scared of rejection (think I doomed myself with this actually as I own a house and would have to be the one inviting really!)

I wouldn't bring up the moving in thing for now, as she is transitioning between jobs (stressful for anyone!). But if you are an hour apart, it might be worth thinking of on your own how the location change will affect one or both of you in regards to work.

She wouldn't tell you her door is always open if she doesn't mean it. Do you have a set of keys to her place? Maybe you could try asking for that, so that you could always come and stay with her for a few days when you don't have work. That way you could come and go while she's at work still.

So it wouldn't be moving in but could help feel things out without as much pressure. As well as showing that you want to spend time with her and aren't resentful (I know you aren't but that might be where my own brain would go) of her working so much. Cause if you're there for a few days, it wouldn't be like you were driving an hour there and back just to see her briefly between jobs. Does that make sense at all?