Well, Dick Tracy has been operating in Chicago since 1931. Any town that can produce crooks like Pruneface and Flattop and Shakey and Influence and Johnny Scorn would have no problem coming up with a Joker and a Penguin.
Map Of Metropolis, plus statistical data.
Scroll down for data.
It’s weird in that, if the Manor is not on the island, it leads one to wonder if Batman has to take a bridge to fight crime in Gotham proper- which opens the door to all sorts of questions about paying tolls, like ‘how does he carry change in the Batsuit,’ and ‘how does that thing fit through a tollbooth,’ and to questions about getting stuck in traffic like ‘gee, wouldn’t the Batmobile would be a real attention-getter if you were bumper-to-bumper for 35 minutes on the Gotham bridge,’ and ‘why don’t the criminal just do commit their crimes at rush hour so Batman will get stuck in a traffic jam?’ 
Not a prob. He just has Oracle feed him the traffic report, and if it’s too heavy, he takes the Batcopter, then if he needs to travel on the ground, he just switches to one of the Batmobiles he has in auxiallary Batcaves around the city.
As for the toll both, he probably has some deal with the highway department where he buys a monthly pass, so if the toll booth attendant sees the Batmobile coming, they just raise the gates and let him through.
Or the Batcave (or at least the exit tunnel) extends under the straight between Gotham and the mainland.
There is such a thing as a sudden traffic jam, and even if the traffic is moderate, the Batmobile probably causes some bottlenecking. Maybe the city has a “move to the right if you see the Batmobile” law like some places do for fire engines… unlike the fire engine laws, I hope for Batman’s sake people actually pay attention to that.
Does he actually have auxiliary Batmobiles?
Tengu, that’s possible, although I think it’d have to be a huge-ass cave and/or tunnel.
Also: 
The dude’s a multi-billionaire. You think he can’t afford more than one car?
I’m sure he can, I was just asking if any of the comics had thought to include that. Would’ve been pretty clever.
He does indeed, I believe. The only related item I can remember seeing, though, is that Robin had an auxiliary Batmobile stashed near Titans Tower. When asked by the others how he’d gotten the money to arrange it, he said he’d diverted some funds from the batarang budget.
UPDATE
I’m rereading Hush, and there’s a page where Batman and Robin take the Batmobile into Gotham. Apparently, he’s about 14 miles from Gotham City, and he DOES have to take the bridge to get there. From the picture, it looks like it’s a one-way bridge, too. For any that are curious, it’s page 12 of Batman #615.