Also helps that he actively runs charities, hires ex-cons and has multiple programs/foundations aimed at reducing poverty. He also makes it a habit (as batman) to just talk to folks. If anything, Bruce H A T E S the idle rich almost as much as he hates criminals. Doesn't help there's overlap.
I saw somewhere as well where he made sure everyone working for Wayne Tech has incredible benefits, and is paid a good wage.
It doesn't help that the Batman begins series is the most popular version of batman for non comic book fans. In that series he does do military work. They also cut out the good Bruce does to make him a stereotypical playboy
The charities are a cover. It's classic charity-washing.