Hi there,
Covering the chips is not necessary. The green matter in the bed will help the chips break down.
If you were so inclined, maybe consider a mushroom species to help the
compost process. I personally recommend wine caps, but the cedar could be an issue. How much cedar is in there?
Even if you cannot find wine caps, some fungus will start and that is a good thing for composting. Try to leave the chips undisturbed so as to not interfere with fungal activity.
I would think about getting some plant started immediately. It could be a nitrogen fixer like beans (now in the heat of summer) or peas once things cool off. Or you could plant something like small plants of tomatoes or squash. If you go the latter route I would dig little fertile holes. The benefit is that the plants and micro organisms will work together to break down that wood.
If you go the fertile hole method you can use the bed immediately. I really like to use tomatoes during the first year as they grow well in the fertile hole, spread roots into the surrounding chips and provide shade to help out decomposes as well as help prevent evaporation.
I have had good luck with this technique in the past, but this is only an introduction. If you have any other questions, please ask.
Let us know how things work out,
Eric