Put something down on the smoker that will provide a way for rain to roll off, a brick or something. Then the cover and then the trash bag and you will have a great set up.
I have a cover from Coversandall - it’s made out of sunbrella, so breathable and waterproof. I have three of these covers, for my gasser, Weber kettle and the 3D. Two of the three are completely under the patio but my gasser is exposed and the cover is holding up well after three years.