We're not good Christian people

We three were walking down the street yesterday morning, and this small lady just comes up to us and asks for a group hug. It was really sudden, so Antonio and I just went for it, and DJ patted her on the back. Then she offered to sell us a freaky movie on a DVD. She just needed money for food.
It's difficult a lot of times how people begging need to be creative to get people to give them money. I tend to just give money away because 1) I don't need the money I have in my wallet at that moment and 2) if you have the guts to go up to a stranger and ask for money (AND offer a freaky movie in return), then you're pretty bomb in my book. Those are probably terrible reasons for me giving money to people, but it's also hard for me to understand how my voting or working for certain organizations can help the same people in a direct way. It seems like bureaucracy gets in the way of resources that people need from getting to them. There are certain places and organizations (Centenary that FeedSTL works with, What's Up magazine, St. Patrick Center/McMurphy's Grill) that affect homeless or needy people in a direct and constructive way, but waiting for policy change is so frustrating and seems indirect.
It might be that I'm impatient (even if I'm officially the patient one) and rather hand someone money than not, saying handing out things doesn't help the poor, and policy changes will be able to deal with the poverty problem in a better and more efficient way.