"Butch is in the shower" or "Butch is taking a shower" would be the most common ways to say it. ) "Butch is washing up" would more likely be used to mean that he was washing his hands and face, or maybe more than that, but not in a shower or bath. You might "wash up" at the bathroom sink, or at the water trough outside on a ranch or farm, or at the edge of a river.
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