Targeted training on the bike can also be very effective in strengthening your cycling muscles and training them to fire properly. I do three pedaling drills:

FastPedal: pedal in a very low gear at the highest rpm you can sustain for as long as you can do it. You have to have some flat road or a trainer or rollers to do this. Don't go fast at all. Ride much more slowly than you normally would, just at a very high cadence. Work up to 15 minutes steady, then 20, then 30, then 40, which might take a couple of years. You should be working fairly hard, but not breathing heavily. If you have cadence on your computer, you are shooting for 115-120. One drill/week.

One legged pedaling: Prop one leg in the frame triangle and pedal with the other. Choose a gear and cadence that allows you to do this without ever letting the chain go slack. Alternate legs. Try to hold it for one minute each leg, then 2 minutes each leg. Do several sets until you can't do it anymore, then continue your normal ride. Repeat next week. You'll get a lot better at it in about 8 weeks.

Then do muscle tension intervals: On a long shallow hill, maybe 4%, shift into a big gear and pedal up it at a very slow cadence, seated. You should be working hard enough to be breathing heavily. Hold your upper body completely still. Do it for 10 minutes, roll down and repeat, 3 times. Continue with your normal ride.

All the above will increase your cycling-specific strength.