Yes, the bleach will clear up the water. As it kills algae, your pool will get less and less green, although the dead algae often clouds up the water. Is there any debris on the bottom of the pool? If so, net it out. If not, just keep socking it with bleach for now and backwashing whenever your filter pressure rises 8-10 psi over your clean filter pressure.

How many times a day are you testing your water? You need to do so at least twice (and 3 times) per day is even better. Each time, add more bleach. The key to killing algae is to sustain high chlorine readings. If you don't, it will take forever to clear the pool. You don't want to shock it and then let it fall way off before dosing it again with more bleach. Keep us posted on how it is going.