Bathing and showering is a completely different experience in Japan. In Australia, you get in, wash yourself, and get out. However, in Japan…
A lot of hotels have Western bathrooms available, with modern showers and separate baths. Sometimes, no baths at all. Bathtubs are increasingly common in modern Japanese homes as well, but there are still many small and old apartments in cities that do not have bathtubs, so public bathhouses are common.
There is a high chance you will not have to worry about bathing in a bathhouse, especially if you opt to stay in a modern hotel. If you’re uncomfortable with public bathing and you’ve booked into a ryokan* however, make sure it specifically states that it has either private or communal baths available. The reason I recommend this is because public bathhouses are literally shared baths with the public. In all but the most rural areas, baths are segregated by gender, and customers bathe nude together, many using a small washcloth to cover the genitals. If you’re squeamish about public nudity, your best bet is to go with a modern hotel or a ryokan with a private bathroom.
*Ryokans are traditional Japanese hotels, where you sleep on futons, eat sitting down at a small table and the walls are made of paper. They are generally run by families.