Your water change bucket will work, however, part of treatment is observation and if the bucket is solid in color-that might make observation hard.
Any container will work-I like to use small bare clear containers that can fit in another tank so I can maintain heat-I attach it to the side of my heated tank with duct tape and will either use the lid it came with or plastic veggie wrap to retain heat/humidity over the water.
Personally, I don't worry about any soap residue-but if you worry-just give the container a rinse in vinegar to cut the soap residue-then a good clean water rinse after that.