I don't tend to use a bivy with a tarp. I just use a groundsheet. Sometimes I don't even bother with a tarp.
Yesterday I was camping out in the garden – a Snowline 750 bag on a foam mat and groundsheet. Night temperatures were close to freezing and it was a clear still night. When I woke up there was some condensation/dew on the outside of the bag near the feet but the bag was warm and dry for me.
A little bit of sunshine and the bag was good to go.
A bivy is used under a tarp because the sleeping bag used cannot cope with the conditions. That's all.
A synthetic bag with a DWR or pertex outer will cope very well with most under-tarp conditions and most outdoor dry conditions.
There's no point in buying an ultralight bag if you then have to gift-wrap it in a 'heavy' bivy bag just to use it…
In 2006/7 most of my tarp camping was done with a synthetic bag under just a tarp in all sorts of wet conditions. It was just fine.
This year I've moved over to ultralight down and it does seem to need a little more protection. The DWR-only coating doesn't seem to be quite enough for use under just a tarp – but I'm still testing. I'm trying a number of different scenarios – eg tarp, tarp+bivy and so on and seeing just how much moisture a bag absorbs.
It's not very scientific but I'm jus trying to work out what goes on. The base-line for me was a down bag inside a twin-skin tent where the weight-gain overnight was 50g on a night that was moist but not warm with the chosen bag.
At the other extreme, a fully waterproof bivy bag used with a down sleeping bag had a weight gain of around 100g for one night.
I've yet to get numbers for use with a pertex or DWR bivy bags or a bag under just a tarp – I have a day job…
What I'm trying to do is work out what setup is going to be most resilient for the cold-damp conditions that are typical. I'm interested in the total weight of everything together that provides warmth and shelter at night.