What I do when I want to make a stronger bridge is I start letting out more revealing personal information about myself that's not so deep that I can't snatch the lure back if the person doesn't seem responsive, but if they pick up on it and pursue or self-disclose as well it's a beginning. I also usually do more personal things for the person and give little gifts. This isn't anything that's extravagant, it can be as simple as bringing them a cup of coffee.
I made most of my close friends at college and at work. When I meet my college friends I'd want to spend time with them outside of class or keep in touch with them between semesters. Work friends I do the same thing, meet outside of the place we're forced to be.
So when I want to deepen a connection I do things for the person, I contact them more regularly, I self-disclose at a higher level (reveal my true thoughts, feelings, ideas on a matter, personal problems) and I start emoting on their behalf, more serious/forthcoming, and most importantly I ask them a lot of questions about themselves. I want to see how self-aware they are and how they think.