I am making a rose gold drip on a cake by painting it with luster dust and I was wondering how to set the white chocolate ganache. Once on the cake do I put it in the fridge or leave it at room temp? Will it sweat if I put it in the fridge? How long will it take to set? The last time I tried painting on it it was still soft.

I've put drip cakes in the refrigerator (these are our personal, family cakes that I leave in the refrigerator all the time) and had no problem with them sweating when taken out.  If your cake is very cold, which it should be to make a drip, it only takes a few minutes for it to set up in the fridge.