The thing is, Bruce does do work outside of Gotham, and presumably on an international scale. You don't get to be a multi-billionaire confining your business operations to just one city. Wayne Enterprises has a presence all over the world, and presumably makes all feasible efforts to carry over the progressive mentality of their "parent office" in Gotham.
Meanwhile, Batman occasionally steps out with the Justice League and plays a key role in saving the entire world.
Elected office wouldn't suit Bruce, and in all truth would hamper him because he'd have to answer to legislators, cabinets, etc... It's not just a matter of "do what you want, when you want."
Bruce does compete with Lex on a national scale, but the main issue is that Lex is (supposedly) nearly/just as smart, and actually has more money.