I think friends are based on what you like to do together. They will want to get together with you to do the activity you do together. This is the motivator.

I met a nice woman my age when I moved in. For a long time, we’d just say hi when we’d run into each other. Eventually one of us asked to go for a walk together. We did and had a good time. But neither of us came on too aggressive, to ask to go for a walk too often. We kept occasional contact until a deeper friendship started to build.

Then we started with having wine together in our building. She enjoys that. I’m sure she enjoys my company, but she also like to relax and drink wine.

Now we’ve started going out. Again, she is enjoying the adventure of that. I’m sure she enjoys my company, but her motivator is also that she really enjoys our going out for nightlife. The experience is fun.

Do you see where I’m going with this?

We both gave time and space. We both made some effort without making the other feel bombarded.

I echo what Bill said, but think it does sound a little needy. I would simply say at the end of when you see this friend, “See you soon! Call me when you can!”. Keep it light, easy breezy.