Question: During the nine days can one shower for Shabbos on Thursday night if there won’t be time on Friday?
Answer: Regarding showering in the nine days, the Shulchan Aruch (Siman 551 Se’if 16) quotes two minhogim; the first minhag is to refrain from washing from Rosh Chodesh Av, and the second minhag is to refrain only during the week in which Tisha B’av occurs [prior to Tisha B’av].
The Remo (ibid) writes that the minhag [for Ashkenazim] is to refrain from washing from Rosh Chodesh [as per the first minhag quoted by the Shulchan Aruch] even with cold water. However, the Remo writes that there is a dispensation for Erev Shabbos Chazon, where one is allowed to wash one’s face, hands and feet in cold water, and some allow washing the hair with hot water – if one is accustomed to washing in this fashion every week. The Mishna Berura (s.k. 97) quotes the Chaye Odom who maintains that it is similarly permissible to wash one’s face, hands and feet in hot water – for one who is accustomed to washing every week in this fashion.
Earlier in Orach Chayim, (Siman 260 Se’if 1) the Shulchan Aruch writes that it is a mitzvah to wash oneself with hot water on Erev Shabbos. The Mishna Berura (s.k. 5) writes regarding washing on Thursday, that this is not considered “honour of Shabbos”, unless one is unable to wash on Friday. And in such a situation, it is preferable to wash as close to Shabbos as possible.
Therefore, regarding washing for Shabbos during the nine days, since it is acceptable (albeit not ideal) to wash for Shabbos on Thursday, the same Erev Shabbos dispensations will apply, since one is washing in honour of Shabbos.