Hi there!

Good question, and pretty easy to answer actually. All we have to do is look at Titanic's deck plans which are available to scan here.

If we look on A Deck- we get a pretty good gist of how the bathroom situation with Titanic was set up. You'll see that all the cabins have a washroom and a washbasin and if you look forward of the grand staircase you'll see both bathrooms and lavatories for ladies and gents. It's important to realize that the toilet and the bath were not the same thing and therefore not in the same room. Anything labeled "bath" is literally that, while "lav" would be used for toilet facilities (or in the cabins marked by a W for Washroom or WC).

Titanic settled on this arrangement all the way down. Public bathrooms and lavatories are found in the same spot- forward of the forward staircase- on every landing down to E Deck. E Deck is where you would have found the stewards lavatories and the petty officers lavatories and also three bathrooms aft across from the E Deck barbershop.

Simply scanning through the deck plans shows that bathrooms and lavs were placed stragically in high traffic, public areas - Amidst passenger hallways on B Deck, forward of the second class library on C Deck, in both the first and second class smoking rooms.

Third class had multiple bathrooms and lavatories on F Deck where most of their cabins were situated.

It's important to note that yes, although it seems Titanic's public bathing spaces were not enough for the 3000 she was capable of carrying, they weren't really designed to be. The baths would be used for that, baths, but every cabin was outfitted with a washbasin which would be used for cleaning, shaving, brushing your teeth and hair etc.

A few first class cabins had full private bathrooms at a premium cost, but most simply contained a toilet and a washbasin. If a full bath was desired, any of the large full bathroom areas were available or the Turkish Bath on F Deck for a spa experience, but in general- folks in 1912 were quite fine with a washbasin and hot soapy water.

As for other ships, I can only speak to Titanic really, but much like the rest of her- her bathroom facilities were considered at worst, ordinary and expected and at best- absolutely luxurious- which was, of course, advertised as you can see here in the period advertisement :) In the spirit of that ad, it's why First Class/Second Class had access to many more full bathrooms than did third, but again- there wouldn't have been a line up for long, soaking, baths.