Are the smoking room separated from the non-smoking?
All rooms are supposed to be smoke-free to my knowledge. I'm sure mine had been smoked in. I can only suggest asking them to put you in another room if it's obvious your room has been smoked in as mine was.
I do not know if they are but our room was most assuredly not smoked in and we had no trace. Wife is extraordinarily sensitive to it too.
We only requested a non smoking room don't know if they have any smoking rooms
Get an answer from Red Roof Inn Asheville - Biltmore West staff and past guests.