It doesn't happen often, especially as you grow older, but when it does, you should throw caution (and nerves) to the wind and pursue it. Sometimes it doesn't happen right away, and that's okay. If it's meant to be, your paths will cross again and boom.
I call that the Holy Spirit at work, but it doesn't matter what you call it -- fate, destiny, whatever. What matters is this: you keep yourself open. If you close yourself, turn inward and hide, then let me tell you you're missing out on wonderful connections, even in this crazy, misguided world.