WB fabric needs some heat inside to drive water vapor out. A WB bag on top of your pack on a cloudy, rainy day will not get warm enough. On a clear, sunny day, the WB fabric would be worse than letting the vagrant zephyrs and sunlight dry the wood. And if the Bush Buddy works at all like other small, enclosed wood stoves, you can burn wood that is a little wet. It will smoke a lot, but it will burn. Some fire starter in the form of dry wood, pitch pine, or maybe a little alcohol doesn't hurt for getting it going. The best bet is to look for dry wood - which you can find even in rainy woods. The small branches on the lower trunks of conifers, twigs with loose bark that strips off easily, things like that. You only need a couple of hands full for a small, enclosed stove.
Yeah, use the extra fabric for gaiters.