No, you are definitely not being a dumbass. You're doing it right. There are two limiters in cycling, breathing rate and leg exhaustion. Cadence increases breathing rate and decreases leg effort. Because air is a free resource and leg effort is limited, cyclists favor a higher cadence than seems logical when one is starting out. Even when your legs are completely beat, you can still breathe fast, get plenty of air, if you see what I mean. High cadence saves your legs. But right now, not so much, because you can't spin almost effortlessly. That takes a lot of practice.
You don't really need a power meter to do any of this. I got quite fast, did and still do a lot of long distance cycling, all without a PM. I did use a heart rate monitor to help me limit my efforts, which is the key to long distance cycling, a PM being almost useless for that. Anyway, drills are how you get good at pedaling.
Gym bikes, that is spin bikes, are all what cyclists call "fixed." There's no freewheel, i.e. ratchet in the rear hub. Thus in a way, the gym bike's flywheel pushes your feet around the circle, which is a big difference. Nonetheless, since you have access to a spin bike, do some high cadence drills on it. Try to pedal at a steady 120 cadence for 15 minutes or so, without bouncing on the saddle. The resistance should be as low as necessary to be able to do that and keep your breathing rate reasonable so that you don't blow up. The secret to not bouncing in the saddle is to work very hard mentally to put force on the pedals only tangent to the pedal circle, IOW, don't push down except at that instant when the crank is level, rather follow the pedal around the circle. Pretend your cranks are turbine blades and make them go around by spinning the blades.
So . . .when you can do that on the gym bike, try it on your road bike. Try to do 1/2 hour of pedaling at a 100 cadence, just enough effort that you are breathing deeply and a bit fast, but definitely not panting. That will absolutely fry your legs, but that's the whole idea. Try that once a week until you can do it no problem. Then do 2 X 25' with a 5 minute rest between, also once a week for maybe 2 weeks. Then you'll have legs and pedaling and can really train. Cycling is a pedaling sport.
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