IMO, vinegar is an unnecessary step. I haven't used vinegar myself, but know others who spray acetic acid on driveway weeds. Haven't heard of using it to kill a whole bed. First, can your grass be killed using the smother method? Super easy and will add organic matter to your bed's soil. check out this link http://www.nwedible.com/2012/02/stop-ripping-up-your-lawn-to-grow-veggies.html If you live in the south and have bermuda grass or some other grass that will come right back after smothering, there's no way to avoid digging all the underground runners out. So why not just ahead and dig? Good luck!

Vinegar works, but not well. You're better off just digging it up to begin with - especially if you're gonna dig it up anyways. Why damage the soil if you don't have to?