what to use for bivy bottom

Silnylon is not too slippery. Allow enough room to put your pad inside the bivy, then slipping off of it won't be a problem. Allow enough material on the top to allow for the loft of your bag and the height of your pad. You do not want the top to be compressing your sleeping bag.
Cuben should be okay for a ground cover. The only cuben fiber I have is on a pack and I would think it might be quite noisy to sleep on it. It would be like lying on crumples up newspaper!

The bivy would be your ground cover. Before a bivy, I used a piece of coated nylon just slightly larger than my sleeping bag. No need for the ground cover to cover the entire area under your tarp or tent. I prefer being floorless.