I put the pad outside the bivy. I use a closed-sell foam pad so it's impervious to thorns and rocks, but as long as you clear the site of sticks and other debris, you could use any pad you want. I always chuckle when I see people carrying their Termarests in waterproof stuffsacks. These things don't absorb water in the first place and even if you were using a tent, there's no rule saying you can't use a wet pad: just put it under (outside) of the tent body itself.
I made my own bivy with silnylon on the bottom and lightweight DWR ripstop for the top. The opening mechanism is a center-oriented zipper so in bug season I can keep the ants, centipedes, snakes and whatnot sealed out of my bag. The zipper does not have to be center-oriented, though. The top of the bivy that covers my face is made of bug netting so when I have the zipper completely closed, I'm not sealed within a ripstop coffin–there is a drawback to this though. That is, if it's a windy night and you have no way to block the wind from your face, you're lips could chap pretty quickly. The silnylon bottom is waterproof, but I always use a thin plastic groundsheet under my tarp to keep it dry and clean, in addition to the rest of my gear I spread around under the tarp (Gossamer Gear polycro groundcloth).
As for tarps, the moment that decided me (actually it was several moments on different days) was when I was in a little solo tent out in the middle of nowhere and passed many excruciating moments listening to animals make noises in camp. Squirrels and birds are common camp visitors that can make the loudest noises, but if you don't have line-of-sight, it's easy to imagine them being bears. I've also woken up to hear a large animal, probably a deer, startle from a resting position not 10 feet from my tent and bound away into the woods. I always thought it was a waste not to be able to know what's going on around me in camp while I am, after all, on a camping trip to connect with nature. Usually the things that "go bump in the night" are products of imagination anyway and so being able to see for myself helps to put me at ease–since reality is almost never as scary as one's own imagination.
You'll get over your fear of sleeping out in the open after a few nights. It helps if you go to an area where you know animals will be making noises so you can feel what it's like to be so exposed and still get to sleep. The first night I tarped, there was a group of elk bugling nearby for half the night and I also heard a pack of coyotes very close. However, I didn't die and I've always figured that was a good sign.