Being from Alberta you know when the first snow starts to fall in those parts. Weather will be the biggest variable until you get out of the higher elevations and more south. It seems like the most direct route south is I-15 then cut over on either I-90 or I-80 and point it toward St. Louis, then south from there over into TN. Keep an atlas handy because you have many choices in routes to take. The best one is a matter of opinion.
Any particular area of TN you interested in seeing? Memphis, Nashville, Pigeon Forge and Gatlinburg? Color is mid October to mid November and we still have some lingering here yet, but the trees are losing their leaves fast now. Weather could be a bit cool for bike riding unless you are perpared for it.