I have a body-taper cut ridgerest that serves as the bottom of a summer top-quilt set up. I used velcro tape on the bottom of the pad, and single layer fabric 'wings' from the quilt has mating no-snag velcro. The wings are the entire perimeter of the quilt except for the neck opening area. I've even created a half length zipper with velcro that I can mate in when I want the convenience of a zip. Velcro spacing is 4-6".
The pad can handle some ground water as the ridgerest is fairly thick, and the wings are silnylon so they don't absorb water. I don't know how a thinner pad would do if a stream of water found it's way along the pad. It's not as convenient as a true bivy to set up because of attaching the bag to the pad with many velcro points (otherwise drafts become a problem. For a bivy you could leave the top attached to the foam. Other than velcro tape, I don't know how you attach a bivy top to a foam bottom; maybe some kind of glue?
I've been considering a 1/8" foam floor to use with a torsolite pad and my pack pad, but getting a piece 72" x 20" requires me to buy a whole sheet, and I haven't committed to doing that yet. It'd be better if the foam has a skin on it, like the ridgerest. The Gossamer gear 3/8" closed cell eva foam pad I have seems to have exposed pores on both sides that would hold surface water and take longer to dry than a shiny skinned foam. A polycro ground cloth from Gossamer gear might also be useful.
As long as your bivy isn't for weathering killer storms in exposed alpine areas, this may work for you. But the weight of a 72" by 20" piece of silnylon witn a taper along the foot is only about 1.5 oz. Add a little silnet inside for tackiness and the weight is still under 2 oz. For a true bivy I think I'd prefer a fabric floor. The silnylon is staticy and picks up dust worse than a pad, but is easily cleaned.