I used to do this, but in an ordinary plastic bag, not Ziplock.

In more recent years, I've carried paper towel squares instead. Far more absorbent, tougher (no unexpected holes!), and can be wet for further cleaning. I've found that they clean better, and the total weight I have to carry is a bit less. Obviously, paper towels are slower to disintegrate, but I pack out my TP either way.
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May your trails be crooked, winding, lonesome, dangerous, leading to the most amazing view--E. Abbey