I have a 3 gallon bucket and I dilute my chlorine with water before taking it to the pool. That isn't necessary, but it makes me feel better....
This is almost the exact technique that I use. I take my 5 gallon bucket, and fill it with about 3-4 gallons of water. I then pour in bleach. I will put in about 24 ounces per bucket. I then slowly dumb that diluted bucket in front of a return. As soon as the bucket is empty, I quickly drop the 5 gallon bucket into the water, fill it, then pour it back into the pool, repeating once or twice. By rapidly filling adn pouring the bucket with pool water, I create a lot of waves int eh pool, so it gets the bleach mixed up.
I know this is overkill, but that is my style.
If you want to pour bleach directly in, pour it slowly in front of a return that is turned ON. But dont pour it at the edge of the pool, so that the bleach sits right on the liner. Reach your arm out, and pour the bleach a few feet away from the walls. Well, as far as yoru arm will reach AND you feel comfortable that you will not fall into the pool.
With either technique, add the bleach in front of the return that is in the deepest end of the pool. Bleach is heavy and will sink, so if your return is in 3 feet of water, then the bleach might reach teh floor. BUt if the return is in 6 feet fo water, if is less likley to bottom out and sit on the bottom of the pool.