I agree, Tom - a bivy without a tarp is not something I'd ever consider. As someone earlier said, it's a shelter for an unplanned night out (or where the plan is to be uncomfortable in the rain.)
If bugs were not an issue, I'd probably still be camping with a tarp and groundcloth. But, for me at least, bug season means some kind of bug netting around me. Back in the day, a bivy was a fairly efficient equivalent for a groundcloth and bug protection, with the added bonus that (unless you were using an all-mesh bivy) it would keep your bag dry if any rain blew in under the tarp. But the tarp was always the main roof; without it, in the rain, a bivy just isn't very livable.
My favorite bivy was the Integral Designs Salathe. It had a full waterproof-breathable cover, and a panel of that fabric could be unzipped to the waist on a warm, dry night because it was backed by a panel of mesh. That gave decent ventilation, but still nothing like the full-mesh Hubba I replaced it with. (Plus, I could actually sit up in a tent!)