Hi! I just read a thread on this site where a guy put a rootless orchid in a more open medium - bark. He watered it every other day and used MSU fertilizer. And after a few weeks, it grew roots.
This is in contrast with something I read that you have to under-water the orchid so that it will grow roots because it will go looking for water.
Do you have any pictures of your plant that you can post? There are plenty of people here that can help you with your plant if we can get a little more information about it.
A plant with no roots has no way to take up water.
The amount of watering done has absolutely no influence on root growth at that point.
The key is to put the plant in conditions in which it will grow rapidly (that's often warmer), but will not desiccate while it awaits the new root growth (that mans high humidity).
I also don't necessarily agree that withholding watering can foster greater root growth. If that was the case, than the opposite would also be true, that lots of water availability should reduce root growth. If you've ever grown a plant well in S/H culture, you know that is simply wrong!