As Lavy said, if you run, you'll only get as far as the security post, and your only chance of going to the Asian side will be if they decide to interrogate you there.
If you're in a car and you cross to the Asian side during rush hour, I highly doubt you'll have the motivation to cross back to the European side on the same day.
Well, y'all work on this ok? It may be a year or 4 until I get to Turkey. I fully expect you guys to have fixed this so I can scamper freely across the bridge when I get there.
