I suppose you either like to do this or not. I believe we all can carry and support 10-20 really close personal relationships with the balance being casual/professional acquaintances. Beyond these casual/professional acquaintances are those with whom we would like to build a relationship. Someone we admire, someone we are trying to sell to, or generally seeking some benefit from having a relationship.
I have always been interested in meeting new people and the older I get the more this interests me. I have overcome whatever shyness I had a long time ago as I realized that being proactive and tenacious will create more opportunities plus you will always learn something from these encounters.
Asking for someone's time is a bit intrusive. After all, I am asking for something that you have a finite amount of and unless you too are interested in meeting new people for the sake of it, then you see these opportunities as a waste of time.
"Networking" is a overused word and you don't just start contacting people when you need something. My goal is to always ask what I can do for the person with whom I am meeting and try to make these meetings part of my regular schedule. One great benefit of blogging is meeting new people be it through a comment, an email, or a face to face. Believe it or not, the more you do for others, the more will be done for you.
I am sharing all of this as I was recently rebuffed after asking for someone's time. I did so at the recommendation of a friend and without a clear agenda or "ask" in mind because I really didn't have either. Yes, you can fault me for that as it is different than my approach to formal meetings but this was not a formal meeting request.
Twenty minutes to shake hands, put a face with a name, and add someone new to my professional acquaintance list was my goal and I believed this person was open to these types of connections.
Clearly, he was not. As I thought more about it and reflected on the lengthy response to my inquiry (which actually probably took more than 20 minutes to write) which laid out his frustration and, quite frankly, resentment of being approached without a specific reason relevant to him, it became clear that either he didn't like to meet new people or his interest in such meetings had been tapped out long ago.
From my perspective, 20 minutes is not a great deal of time in the big picture and you never know where a new relationship will lead but keep in mind this perspective must be shared by the person from whom you are requesting time