First of all, as you say, pulling turfgrass is a PIA, because it forms mats of sod. Time consuming and obnoxious.
How big is the area? Could you once again turn it over by hand, using a fork or spade, burying the sod on the bottom? Or, would that be too much work due to the size.
Another way to go -- roundup or a similar herbicide with short duration. The reason your grass came back is because its probably a cool season grass that sprouted from seeds. It's also possible your first application of herbicide didn't give total kill, and some survived to regrow - two applications spread a few weeks apart should get the survivors of the first round. I know a lot of people are against Roundup, but it does have its uses. One advantage is that it appears not to have long-term residual effect in the soil.
Another option, maybe - cover it all over with black plastic -- that should kill off anything under there in about 2-3 weeks.
And no, bleach doesn't kill plants for the most part. It may burn the tops, but it won't kill them long-term.