I have solar and it keeps my pool about 5-10° warmer than it would be otherwise. I don't use a cover, I expect I could do better if I did. Those temps are mostly true in the middle of pool season, and less true in the cooler fringe months (mostly due to sun angle on the panels). We're still in a bit of a heat wave here, so my pool is still very swimmable. I just asked my neighbor last week about his pool temp, and his was 10° less than mine. He doesn't heat his pool. Which means for this month, I have a pool and he doesn't. Yay solar!
Do you have any neighbors with solar-heated pools? To ask how their solar is working for them? A distant second is to ask a local solar heater installer what to expect (they'll exaggerate). The point was, to gather some real-world data about how solar, or heat pump, or gas heat is going to work where you live, and what each might cost to install, maintain, and run. In addition to what you gather here, you need some local opinions, too.
PS. I'm with Jim. If I had a cover, I'd just look at it. I'd never actually swim in my pool! Waaaaay too lazy to cover a pool. I give up some swim season days rather than deal with a pool cover. And I have a gas heater that I have never turned on. Gas is too expensive for my pool budget. Which is the other reason I don't use a cover. If I can't swim in it, I can still look at the water, which I really enjoy, all year-round. A bubble cover? Not so much...