According to what I have read, bathing in Japan started in 538 AD, when Buddhism arrived in Japan. Apparently, Buddha's said, "Bathing rids seven illnesses and brings seven lucks," Consequently, Buddhist temples built bathhouses. Since then, the custom of bathing started in Japan.

Hot thermal springs and temple baths are considered sacred waters with the power to heal and purify. I think you will find a comparative number of cultures with healing, purification, and sacred waters in their religious traditions.

Public baths (Sento) have been around for about 400 years and are believed to have originated from the Buddhist bathhouses, where people took bath together. During their bathing, people talked about their day-to-day lives, and gossiped. Over time, bathhouses became important places for communication.

Bathing started as a means to soothe the body tired from traveling and to prevent illnesses. The tradition spread widely and deeply into the lives of Japanese and continues until today. Mixed gender bathing is called (kon-yoku) and in the 19th Century the government prohibited it, although as I said earlier it did exist in some places only 10 years ago.

Japan has plentiful water and many natural hot springs (onsen). Most major hot springs in Japan (which has over 23,000 hot springs, two-thirds of the world's total) were by legend, discovered by Buddhist monks (Kôbô Daishi, Gyôki, Ippen Shônin) often guided by Buddhist deities (Yakushi, Kannon, Jizô), while the Japanese practice of bathing originated in the temple baths of Tôdaiji, Saidaiji, and Daigoji
The expression "hadaka no tsukiai" Literally means "naked companionship." As with many Japanese words, however, the true meaning is a friendship with frank communication, socializing without hiding anything.
For the Japanese, bathing means not only washing themselves, but also relaxing both mentally and physically..

By the way, the bathrobe is a cotton dressing gown called a yukata.

Public bathhouses are still found everywhere in Japan, but the numbers are significantly decreasing year by year. The bathing fee is around 300 - 400 yen (2.5 - 3.3 USD).