Seriously, what kind of bumpy roads are we talking about?
I'm trying to figure that out myself. On my commute, the answer seems to be "not very", or maybe "it doesn't matter."
The primary driver of lower RR is inflation pressure (and that includes changing tire size, though smaller tires should have higher RR.) but the differences are so minor that it's almost not worth worrying about. At reasonable speed, running a larger tire at 75 PSI is so close to running a rubber band of death at 145 PSI that it's not worth the effort. On rollers, the RBOD is consuming ~30 watts versus ~40 watts (but that's out of 250-300 watts total, less than 10%.) On a real road, they are probably comparable, and my tests seem to bear that out. My commute is very consistently 1:15-1:20. Swapping between those tires makes no discernable difference in commute times.
In comfort and flat resistance, the difference is VAST.