How long does it take for a solar cover to heat up a pool?

It depends on the size of your pool, the number of panels, your location and the desired temperature gain.

Assuming my panels are equal to the sf of the surface area of my pool in (for example) North Carolina I can expect to see about a 1 degree rise per hour using a blanket during the sun, so when you first turn on a solar system it can take 3-5 days to fully heat your system but once it reaches that point it keeps it warm from then on.