How gonzo would I have to be to position a bicycle at one end of the Wapack trail and then ride the bicycle back to my car at the other? Any unavoidable hills that I'd hate facing after a long hike?
Depends on what kind of ride you're looking for and in which direction you want to go.
The most direct route from Watatic going north would be to go 119 E, left on Pillsbury Road in Ashby, left on West Rd / 123A, north on 123, follow 123 to the right at the intersection of 124 (near the Windblown XC area), and keep on 123 until it hits 101 and continue on it until it Sand Hill Road and make your way uphill to the northern terminus of the trail. IIRC, this route is a lot of back roads that see minimal traffic, but there is really no designated shoulder to ride on in most places, some sections were quite bumpy last time I drove it, and there's a lot of little up-and-down hills to contend with, including a nasty climb in New Ipswich after you pick up 123. Of course, heading south this wouldn't be a problem. Google maps lists this route at 18.2 miles from Mt. Watatic to Sand Hill Road
If it were me, I'd opt for the longer route of 119 West to Rt 202 north in Rindge, and follow 202 all the way to Peterborough. Lots of traffic on that road, but the shoulders are wide (except for a short stretch just before Peterborough), the pavement is in good condition, and the road has a more relaxed grade to it. Google maps give a distance of 22.4 miles from Mt. Watatic to Sand Hill Road in Peterborough.
I would have thought the second route was a lot longer, but considering it's "only" 4 miles, that's the one I would go with. Sounds like a fun hike-and-bike!