I usually sleep without the bivy under my tarp, but... foot-long centipedes? Tarantulas? Deafness? Screw that, I'm going with a fully enclosed tent!
In new england, the worst I've had is slugs on my stuff in the morning, so I find the bivy to be not always necessary. However, if I were camping in a windy area, or during peak bug season, I'd definitely want my bivy around.