This kind of household structure without a bathroom was actually quite common throughout Ancient Japan. The vast majority of urban residents, including Samurai, did not have bathrooms in their homes.
The main reasons for this were twofold.
One: Limited space. Take Edo as an example, the average living space per capita for the townsmen of Edo was less than 10 square meters. Such cramped living conditions barely accommodated people, let alone building a bathroom.
Not to mention a bathroom, most families didn't even have a toilet. They had to share a public toilet with several, or even a dozen, neighboring households.
Two: Fire safety. Bathing always requires heating water, which greatly increases the risk of fire. Therefore, the government did not encourage townspeople to build bathrooms in their homes.
Due to these two reasons, in the entire Ancient Japan, only a few people had the means to have a private bathroom at home. Most people had to go to nearby bathhouses to bathe.
