What's worked for me is just taking "risks." I tend to have that problem where I have work friends that stay at work and never seem to cross over. Then my best friend started a new job and I saw how she quickly turned her work friend into outside friends. I asked her wtf? How'd you do that?
Basically, What it boiled down too is your talking and obviously getting a long so now what? Just take that risk and say "Hey, Give me your number so I can text you this cool thing/mutual interest later." or "I'm doing X later you should come." Or friend aquantences on FB. It gives you something to talk about and can be a less stressful than face to face maybe? I mean it's very situational as to how you'd phrase it, but the basic principle is the same.
I know it's EXTREMELY hard for me to do this, because I'm terrified of rejection. But, I took her advice and it really did help. I always wondered why these people who seemed to like me would never invite me anywhere or connect outside of work/club/whatever. I made the mistake of assuming that they didn't really like me/were just being polite, but once I started putting my self out there (and believe me it was very anxiety provoking) I really started making stronger connections. These people later told me the reason they didn't bridge the gap themselves is because my demenor (my facial expressions and general interactions fueled by my anxiety) made me appear as though it was I who was just being polite and not really interested in being friends outside of work/school.