Here is some first hand experience with using a secondary source of water to flush the toilet. Our toilet water tank cracked and we could not get to Home Depot until the weekend. We were stuck flushing the toilet by pouring water in the bowl.

The two insights I came away with are: you need a big container to pour water so it will flush and a tub full of water is only going to be good for about 20 flushes.

I think if we are in a shelter-in-place situation we will use a bucket toilet with a plastic bag liner and kitty liter. The water would be wasted for flushing the toilet. If you plan to use tub water make sure you have a container that is big enough to cause a flush.