I use a similar strategy to your bowl method.
I carry two half gallon gator-aid bottles. One labeled clean and the other labeled dirty. I scoop up the water with the dirty bottle and then filter it into the clean bottle at my leisure.
I often camp where there is no water. I do so to get away from people. Dry camps are less used than camps near rivers and streams. The two bottle system allows me to carry a gallon of water to my campsite. I filter one bottles worth, scoop up another 2 quarts of dirty water and head for camp.
The two bottle system has also paid dividends in bad weather. I can quickly grab two quarts of dirty water on the way to camp and then filter it in the comfort of my tent.
I have a large pack so carrying two bottles is no problem for me. I sometimes even use a gallon bottle for the dirty water.