Wow, in an intersection even! I'm glad you're okay.

For short rides, if you can stand the metal-on-metal noise, hanging your u-lock off the handlebars or between the top tube and downtube usually does the trick with the least fuss. If you have a belt, through the belt works pretty good too.

If you want to try bungees again, I use a bungee made specifically for rear bike racks. Something like this. It seems a little more foolproof to me than just a bungee, and since there are three straps on one hook, a little more versitile and stable on the bumps as well.