Answered by Shaykh Yusuf Weltch
Question
If I mix an impure cloth with a pure cloth in detergent water and then wash them in a bucket with a small amount of water, are the clothes considered pure?
Answer
In the Name of Allah, the Most Merciful and Compassionate
Filth is divided into two types: 1) perceptible filth and 2) imperceptible filth [Tahtawi/Shurunbulali, Hashiyat Maraqi al-Falah]
Note that filth is perceptible if its essence (not just a quality, like the color) can be seen after drying. [Ibid.]
Perceptible Filth
For perceptible filth to be considered pure, one must remove its essence. This can be done even with one wash and even in a bucket; as long as after the wash, the perceptible filth is no longer there. [Ibn Abidin, Radd al-Muhtar]
Imperceptible Filth
Imperceptible filth, however, is considered pure when sufficiently washed such that one is reasonably sure that the filth is gone. [Ibid.]
The relied upon position is that there is no condition of a specific number of times of washing. If one is reasonably sure the filth is gone after one wash, this is sufficient; some, however, did still make washing thrice a condition. [Ibid.]
Washing in a Bucket
Impure clothing washed in a bucket is considered pure if (a) washed in three different buckets, each with pure water in them, or (b) washed three times in one bucket. [Ibid.]
Note that if you rinsed them out with running water after washing the clothing, the running water is sufficient enough to remove the impurity. After that, merely rinse the bucket out once. [Ibid.]
Hope this helps
Allah knows best
[Shaykh] Yusuf Weltch
Checked and Approved by Shaykh Faraz Rabbani