Esper Mami

Esper Mami is a manga and anime series created by Fujiko Fujio.

Franchise History
Esper Mami started as a 9 volume manga series that ran in Shōnen Big Comic from 1977-82. It was adapted into a 119 episode anime series by Shin-Ei Animation that ran 1987-89 on TV Asahi.

Episode 40
The title character, Mami Sakura, takes a bath with her pet dog Konpoco. First aired on January 12th, 1988.

DVD 15
Source:

Unknown episode
Probably somewhere around episode 87 to 89:

DVD 17
Source:

Unknown episode
Probably somewhere around episode 86 to 101:

Unknown 1
Mami Sakura walks in on Kazuo Takahata in the bath

Unknown 2
Source: Konpoco and Mami`s parents Juro Sakura and Naoko Sakura both walk in on her after she has fallen into the bath tub clothed.