You might find this recent thread helpful.

Cycling uses the legs differently from running. Spinning is a good strategy, but if you want to build leg strength, ride up hills, mainly seated, at cadences of about 60 rpm.

As far as training being structured similarly to running is concerned, I guess so if you were a middle-distance runner who trained speed as well as stamina. It sounds like you can ride for about 8 hours per week. I'd suggest a couple of interval sessions, one of extended 20-minute intervals at the sort of level of effort you'd run 5000 metres, and one of 1minute intervals at the highest intensity you can sustain. Throw in a "tempo" ride of an hour at a runner's 10k level of effort, and make the rest of your rides pretty easy, cruising speed stuff.

If you have any useful hills you might ditch the sprint interval session and incorporate some hard hill repeats into your (otherwise pretty relaxed) 2-hour weekend ride.

If you're riding 20 miles in an hour you're pretty fit. Start to train systematically and you can expect significant improvements, though 8 hours per week is pretty much the minimum if you want to get fit for racing. Were you to set yourself a goal of 40k in an hour, that would be a great achievement in a year. Riding at 25 mph requires almost twice the power of riding at 20 mph, because wind resistance means that the power required varies with the cube of your speed.

I'd strongly recommend a HR monitor, it makes the interval workouts much easier to perform consistently.