While doing a job I kept two 5 gallon buckets at the ready. One had an Oxi Clean mixture for pads, the other a MF cleaning mixture for towels. Each went in the respective solution after I used it.
If I was out of steam at the end of the day (almost always) they could just sit there and keep soaking. The next day I washed the MF towels in the machine and hand washed the many pads used. All ended up considerably cleaner after soaking.
So no I didn`t wash them in a bucket actually but it was part of the process.