Using a tarp to prevent condensation in a bivy?

If you have a tarp suspended above your bivy, two things can happen that could reduce condensation in the bivy; one, the surface of the bivy fabric can be slightly warmer due to some slight reduction in convective heat loss (if there is no breeze); and two, the surface of the bivy fabric can be warmer due to less radiative heat loss (this will happen breeze or no breeze). Warmer fabric will have less condensation.
BUT – Whether you will be able to tell the difference is a whole 'nother question. You may and you may not. How much condensation you get depends on a number of factors including how much heat your body is producing, how much insulation is between you and the bivy fabric, humidity, how much moisture your body is producing, the amount of airlfow over the exterior of the bivy, the breathability of the bivy fabric, the air temperature, etc.. So if you happen to be in conditions where all of the factors combine to push you just over the line into condensation occurring without the tarp, then adding the tarp may pull you back from the brink (as it were). But if you are well over the line then having the tarp will probably not make a noticeable difference.

That can be a bit of a myth. If the surface of your bivy bag reaches condensation temperature, then you will get wet, tarp or no tarp.

However, a tarp overhead will reduce the amount of IR radiation loss to the sky. This may, sometimes, mean your bivy bag will not cool down far enough for condensation to happen. This haoppens especially on those clear nights.

That said, if there's a cold wind blowing under the tarp, the benefit of the tarp may be almost zero.

Cheers

Staying Dry in a Bivy Sack: Techniques for Managing the Moisture Balance Between External Precipitation and Internal Condensation

Night Time Condensation on Tarp and Tent Fabrics

The tarp does help some on really clear nights when radiative heat loss is highest but the colder the night or overcast and cold the less the effect of a tarp or other layer over you. My piece on condensation has many links to explore on the subject.