Originally Posted by
Carbonfiberboy
.....Nothing to do with the rearward force from bumps because for every rearward force there's a forward force from the other side of a random bump. Rough roller test show that resistance decreases with increasing pressure just the same as it does on smooth rollers. It's the upward movement of the bike that uses energy, so to get an increase in resistance there has to be enough upward movement to counteract the inherent lower resistance of higher pressure. .
I bolded the main part of your error. There's no return of energy lost to the rear vector of the force needed to raise the bike over the bump because the bicycle is moving too fast and "ski jumps" off the other end of the bump and free falls back to earth.
You are right that the energy lost on bumpy roads relates to what's needed to raise the bike, but it's not the vertical movement that's an issue, it's the rear vector of that lifting force generated at the point of contact.