You don't want to let a pool with a liner dry out. The liner can shrink and not have enough flex remaining to expand again.
We normally recommend leaving at least 1 foot of water in a pool if a refill is needed. With clean, sanitized pool water, most algae will scrub off with a standard brush.
As far as bleach, most of us use gallons of bleach (or stronger 12.5% liquid shock) each month as the chlorine necessary to keep a pool sanitized and algae-free. Plain Bleach is liquid chlorine plus water. Pool store chlorine tabs or power contains chlorine plus extra chemicals you don't want in your pool. You don't want full strength chlorine sitting in the liner, so you will want it diluted as you scrub.