In Catelyn POV in the first book we know that Lady Catelyn reached from Kings Landing to the Trident crossroads in 14 days. We learn the location at (p 277):
"It was dark when they reached it, at the crossroads north of the confluence of the Trident."
And the time it takes at (p 280):
"We left Kings Landing a fortnight ago, Catelyn replied, answering the safest of his questions."
In a weird way, Lady Catelyn and Ser Rodrik perfectly fits your definition. It appears the distance between Moat Cailin and Mole Town is about 2.5 times that of Kings Landing and the Crossroad Inn.
We also know that (p 278):
"For the past week, travelers thick as flies upon the Kingsroad; knights and free riders, singers with their harps and drums, heavy wagons laden hops or corn or casks of honey, traders and craftsmen and whores and all of them moving south."
- Catelyn Stark is not a great rider.
- They travel at the end of the summer/beginning of the autumn. It is faster than winter.
- The roads being crowded reduces the speed.
- The roads are in a better condition than they are in the North, simply because they are used much more often.
The assumptions 1 and 3 reduces speed while 2 and 4 increases the speed. However I tend to believe that "thick as flies" implies that effect of 3 is greater than others, so they traveled slower than someone might travel in early winter from Moat Cailin to Mole Town.
So my answer would be 20-25 days. (Page numbers may vary, depending on the edition.)