I used a tyvek ground cover with my tarp last year on a 5 day thru hike of the Foothills Trail, during which it rained for 3 days/night straight. One night there was severe thunderstorms moving through my area.
I glued a foot pocket at the foot of the cloth using another piece of tyvek and super glue. I figured it would help to keep my bag in place during the night.

The super glue (cheapy dollar store brand) worked very well.
The bottom is folded along the line you can see, and the little tabs were just folded over the little half oval shape, and glued a couple at a time. Made sure that the pocket was just narrow enough to "bathtub" the end of the tyvek a little and tall enough not to compress the down. This pocket is too small for my winter bag, but worked great on my 14oz top bag.

In practice, it allowed me to keep my head well in from the edge of the tarp, and not worry that my feet were poking at the other end. Not only did it protect the foot of my down bag from blowing rain, but the tyvek also withstood the 1/4 – 1/2" deep puddle that I slept in during hardest periods of rain.
After the thunder died down and I got some sleep, I awoke to a dry bag. There was quite a bit of sand that splashed up on it from the puddle, but the DWR finish handled that fine. This thing worked well and weighs about 4.5oz.
It is my opinion however that tyvek won't breath well enough for a complete bivy. I hope I'm wrong.