I have a problem. I've worked hard to beat anxiety and become better at approaching people and starting conversation. The problem is that I find it hard actually going beyond shallow conversation and developing a more personal connection with women. I guess this may come under the category of flirting but sometimes I meet women in situations where flirting may not be acceptable straight off the bat. Or at least I feel that I should know them a bit more before flirting. I know people who are able to make good friends with people and come off very warm. In contrast, sometimes I feel a bit robotic. How do I get more personal with people? How do I go from an acquaintance to a close friend or partner?

Edit: To give an example of my problem: A woman I know recently said we'd probably be good friends and should hang out more. I agreed and we chatted a bit via text but eventually that died down. How do you ask someone out to do stuff? Im not interested in making it a date but just doing something together as buddies to progress our relationship? How do you make the leap?