Lesbian relationship advise needed!
About a month ago, I met a girl and we had some nice firendly hangouts. She made it clear that she's interested in me and likes me, however never attampted to kiss me or anything. Very soon she invited me to travel to a city where she went to university at. I agreed, expecting that things will happen there between us - considering the interest she was expressing.

We shared same bed for 5 nights during the trip but nothing. When we came back, we kept hanging out and she was still expressing interest. Few times we were drinking and started talking about that trip. She explained to me that I was her guest there (& therefore had a free accommodation) and she didn't want to make me uncomfortable by making a move, didn't want me to feel like she invited me just for that.
Recently, we got drunk in the park and she was very clear about liking me, so I kissed her and we spent a long time making out. I am not an initiative person and when I am sober, I feel very shy to make a move. She mentioned that she's usually not shy but feels shy with me because she likes me a lot.

After that, I've invited her over and gave her a massage (sober) - again, nothing happened! Just lots of massage and conversation... I offered her to stay but she didn't, saying that she didn't bring her toothbrush pijamas etc. Meanwhile, she 's inviting me to go on a trip together again and made it clear that she isn't into seeing other people, it's been a while since she felt so interested in someone, even mentioned we should do something special when it's 1 month since we've met each other.

I feel quite confused; I am used to people being proactive in sex, making a move - usually on the 2nd or even 1st date. With this person, I don't know what to do. I don't wanna be the one asking for sex or making a move (old-fashioned gender roles?); and am even starting to doubt if she likes me enough. I also measure relationship success by sexual chemistry and while I can see that we have it, I find it super strange that there have been So Many opportunities but the person hasn't made a move.
Any advise appreciated!