I think that a handheld camera is a disadvantage, making people feel uncomfortable (they are used by journalists that usually expose aspects of peoples private lives). On the contrary, a large (at least MF) camera on a tripod would make people feel less "threatened". You also have to explain why you want their portraits taken and what you'll do with them.
In 2009 our photography group, "Overexposed" organized a group project, called "Sunday Times". We decided to go to different parts of the city every Sunday with a Hasselblad on a tripod and try to convince passers-by to pose for a portrait. There were 6-7 persons from our group there every time, some of them female (it helps, hahaha) and we assigned a different job to each one every time we did some shots of a person. So, one would operate the camera, the other would hold the reflector, the other would approach the people that walked by etc. It worked really smoothly and we managed to shoot more than 60 people after a couple of months. We promised to the people that agreed to sit that their pictures would not be exposed in magazines, newspapers or some journalistic site, but would only be used for artistic purposes (an exhibition for instance).
We are now at the final stages of printing (we had some problems with our darkroom for some time) and we'll soon be ready to show the work.
Don't despair, there's always a way to do it !!