Could it be that overnight water is slowly leaking into the combustion chamber? Then after driving it for a wee while you blow out all the water.
Tang0 is right, if it has a slightly blue tint to it then its oil burning, if its just white its water. Check for an oil film in the coolant or for bubbling in the coolant caused by exhaust leak. Another thing to do is an oil change and inspect for a 'milky' effect in the oil. Those are all symptoms of a blown head gasket.