Hello, I have a bit of a problem that's probably a piece of cake for most people, but I am rather shy about.

There is this girl that I've had contact with for about five months now. Since about a month ago, I realized that I actually like her quite a bit. Spending time with her is a lot of fun, and we both share a lot with each other, and at the moment we have built up quite a good friendship, where we see each other about once a month or something. Those meetings are always a lot of fun.

On one hand, she has had a very bad relationship before I met her (she broke up like, half a year ago or something), so she really wants to take her time and wants to take her time in terms of relationships. She also let me know that she has really gotten sick of tons of guys coming over to her with shallow flirting attempts when she suddenly became single again (which I can understand a lot). I myself am just out of a bit of a desperate period in which I was way too actively looking for a relationship. Right now I'm really just trying to have a lot of fun, keeping my expectations low, while keeping my eyes open in case I see someone I like (it's been really difficult, but I thankfully am not as desperate for a relationship as I used to be).

Now having said that, this girl caught my attention and I like her quite a bit, but I have no idea to take this further. I don't want to push anything, and I certainly don't want to be one of those guys who just comes along with those shallow flirting attempts. It's been like that for really most of my life: I like making friends, and my friends really mean a lot to me, but I'm always too afraid to take things further. It's because of that that I've never had a relationship despite being 25 years old.

Does anyone have any tips?