Appleseed

Appleseed is a series that began as a manga that ran from 1985-89. An hour-long OVA was produced concurrently in 1988.

The series was relaunched as a 2004 film, with a 2007 sequel called Appleseed Ex Machina.

Finally a 13-episode anime series called Appleseed XIII began releasing in 2011.

Appleseed (anime film)
In the OVA, the female character Deunan Knute takes a Shower. She is seen walking into the shower clothed, throwing her clothing over the wall and then turning on the water. She is not actually seen while bathing though. Afterward, she mentions to her partner Briareos Hecatonchires that she was late due to having to take a shower. Briareos questions why she did this, since they were seeing a woman and not a man. She explained that was exactly why she had to do it.