Everything you do is just fine.
The easier and nicer way to collect the stones without scooping them out of the toilet bowl is as follows: you empty the contanes of your sieve (after pouring cold water throgh them) into some little flat tank filled with very cold water, and then just skoop your nice clean stones from the surface of the water, it is much more convenient.
I discovered this way when I attempted to make a nice photo of my stones.