The Shulchan Aruch (OC 550:2) says that it is permissible to shower (as well as the four other forbidden pleasures) on all fast days other than Tisha B'Av and Yom Kippur.
The reason says the Mishna Brurah (6) is that when they accepted these Taaneisim upon themselves, they only accepted it for fasting, since all the stringencies of Tisha B'Av would be too difficult for the people to keep. Therefore, says the Mishna Brurah, a Baal Nefesh should keep the stringencies of Tisha B'Av on all the fasts (excluding not wearing shoes and Tashmish B'Lel Tevila).
When do these stringencies apply for those who keep them? The Shaar HaTziyon brings in the name of the Shelah HaKadosh that this applies from nightfall and not only the morning of the fast. The reason is, as the Mishah Brurah points out in (565:9), that although we stop eating only in the morning, the Taanis begins at night. Therefore a Baal Nefesh should abstain from all things prohibited on Tisha B'Av from nightfall according to the Shelah HaKadosh.
The Pischei Tshuvos points out that even those who are machmir on the stringencies of Tisha B'Av from the night before, do not stop eating and drinking the night before as it weakens the body and is not simply a matter of abstaining from pleasure.
Important Note: We bring this tshuvah as a starting point for discussion and not to convey any halacha. We try to convey the Tshuva to the best of our ability. We admit that our understanding may not be accurate. One should learn the tshuva to verify the accuracy of our interpretation. Please understand that this Tshuva may not be the final word on this topic. One should consult a Rav before drawing any conclusions.