By the way, the master suites existed only on PRR's Broadway Limited and Southern's Crescent Limited. No other train, including all the western trains, had showers. Somehow, people survived.
Well said, "somehow we survived". I took several cross country coach trips. Lack of sleep much bigger concern than lack of showers.
And if you were in a sleeper you could strip down and do some washing, just no running water.
After all, if you bathe before the trip begins you are not going to accumulate much "new" dirt.
In addition to the Broadway Limited and the Crescent there was a shower in the sleeping car passenger's lounge car on two or three Southern Pacific trains. This included the Sunset Limited. These showers did not get much publicity but they were in the timetable.
So.....that brings the grand total to about five.
OH WAIT, I think the original CZ had one in a room they called a drawing room. Rather than calling it a master room. But keep in mind that plenty of trains had drawing rooms but none had showers except this one on the CZ.