It all depends on the dew point.
From Wikipedia: "The dew point is the temperature to which a given parcel of air must be cooled, at constant barometric pressure, for water vapor to condense into water. The condensed water is called dew. The dew point is a saturation point.
The dew point is associated with relative humidity. A high relative humidity indicates that the dew point is closer to the current air temperature. Relative humidity of 100% indicates the dew point is equal to the current temperature and the air is maximally saturated with water. When the dew point remains constant and temperature increases, relative humidity will decrease."
The water vapor given off by your body will condense when it reaches something whose temperature is at, or below, the dew point. It has nothing to do with surfaces, per se. Condensation occurs on a surface only if that surface is below the dew point, and everything the water vapor has encountered previously is not.
If the temperature is cold enough for the dew point to be within the down of your sleeping bag (as it may well be in winter), then that is where moisture your body gives off will condense (dampening the down). Otherwise, the condensation will occur further out, if at all.
Note that a clear sky is very cold, and any surface exposed to that clear sky will be cooled by radiation to the sky. If your sleeping bag is exposed to a clear sky, even in the summer, then the outer fabric of your sleeping bag may well be below the dew point — even though the air temperature is not. In that case, it will condense any moisture it comes in contact with — whether body moisture coming out through the sleeping bag, or moisture from the air itself.
If you put a bivy sack around the sleeping bag, then the above comments apply to the bivy sack fabric. If you are in a tent, then the comments apply to the tent. (Note that a well-ventilated tent has lower humidity, and therefore a higher dew point. A tarp is an extremely well-ventilated tent.)
You can avoid the problem by interposing something between your sleep system and the sky, such as a tarp or even tree branches, thus preventing the radiation cooling of the top surface.
Illustration: In the early days of NOLS, one of Papa Paul's teaching points was to just let people throw down where they pleased the first clear night out. Newbies tended to just put a ground cloth in the nice grassy meadow, and sleep on that with a fine view of the starry night sky. They also had wet sleeping bags in the morning.
More experienced people would sleep under the trees at the edge of the meadow, and have dry sleeping bags in the morning. Made the point very effectively and convincingly.
— MV
P.S. Dew does not "fall" — it is the result of moisture from the air condensing on objects that are below the dew point, such as the grass, or your exposed groundcloth or sleeping system.
PPS. The above also explains why dew is (mainly) a clear-night phenomenon — clouds are nowhere near as cold as the clear sky (which is around absolute zero) so there is much less radiation cooling on an overcast night.