You can hook up your equipment and go ahead and start circulating the water while the cover is on. If you need to add bleach, you can do so slowly through the skimmer with the return jet eyeball aimed down while your cover is on the pool. You wouldn't want to shock the pool with the cover on, however, as the fumes could damage the cover.

I no longer cover my pool in the winter, but back when I used to do so, I would do what I explained above. By doing so, I could keep a little chlorine in there and keep the pH in range so algae didn't get started but by having the cover on, it kept the debris from the trees, pollen, etc out so I didn't have to do a lot of cleaning for weeks while it was still too cold to swim.

Is your water clear? Do you have test kit? If not, get a Taylor K-2006. (You can order it from the Amazon link in my signature below.) If you don't have a kit, for now, pick up a cheap OTO kit somewhere (red and yellow drops) and test the chlorine and pH and post the numbers.

In your pool, each quart of 6% bleach will add about 1ppm of chlorine. Let's wait until we see some numbers before we advise how much bleach to add.

One last question, what kind of filter do you have?