That's an uncomfortable scenario.
The biggest thing I've learned about bivy-sackin' is that I've learned never to remain constrained by the types of campsites available to tent- and shelter-campers.
When the weather is nice, you have your pick of campsites, and can sleep on perches tent and tarp campers can only dream about.
And when the weather is nasty - your options likewise expand, for increased comfort.
So, in calm conditions, go for high places and good views. One of my favorite bivy sites was this one, on a knoll below the western faces of the Grand and Middle Tetons, August of 2001. Photo by Alan Dixon.
But when you're expecting inclement weather, or you're otherwise "underdressed" with respect to your sleep clothes / sleeping bag / pad, consider tucking away into the bushes to stay a little warmer. This was my strategy most nights of a stormy trip in the Bob Marshall Wilderness this summer. On one particularly foul night, I tucked deep into the bushes on a small bench, just off the banks of the South Fork Flathead River. I had bushes all around me, touching my bivy - it was almost coffin like. But I stayed warmer, and drier, than if I'd picked the perch that was more aesthetically pleasing - which was on the sandbar overlooking the river.