I don't always bring a bivy, even tho I make them. Like they said, site selection is a big part of tarp camping.
Where a bivy is necessary with a floorless shelter.
Ledges, cliff bases etc where you have no choice in site selection as to prevent water running under the tarp.
High Desert, alpine, tundra etc. where high winds can suck the heat from your sleeping bag or quilt.
Tundra, Swamps etc where bugs can overwhelm a headnet.
Where it is nice.
Desert, Dunes on river trips, to keep blowing sand out of your sleep system.
Dirty campsites to help protect an expensive down bag.
Using a quilt, to keep the edges out of the dirt and prevent drafts.
Storing extra clothes, safe but handy if the night turns cold.