I don't know how robust the waterproof bottom of your bivy bag is, but with the bivy bags I know (which are predominantly some kind of mountaineering emergency equipment) I would not want to put the sleeping pad into them. The reason is simply, that bivy bags are designed to give a good weather insulation (primarily by being waterproof and windproof) while being (more or less) lightweight. A result of the latter point is that they are normally not that robust.
If you now put your sleeping pad into the bivy bag, then the bag is the layer that is directly in contact with the ground and that has to bear most of the friction that arises while you move in your sleep. This won't be a problem if you camp on snow as you have a smooth ground surface there but if you camp on rougher ground, I could imagine that you would wear down the bivy bag rather quickly.
If the bottom part of the bag is actually more like the bottom of an inner tent, i.e. made of some robust plastic foil, that might not hurt that much. In this case it might be better to put the sleeping pad inside so that it does not get dirty.