What is the ruling on the custom of refraining from bathing on Wednesdays for fear of affliction?

What you mentioned about your mother is not based on any Shariah evidence. No day has any effect on bringing about or repelling misfortune or blessings. Wednesday, like any other day, permits ghusl (ritual bathing), and no harm or disliked consequence results from it. Malik was asked about cupping and applying ointments on Saturday and Wednesday, and he said: "There is no harm in that. There is no day but I have been cupped on it, and I do not dislike any of this." Pessimism regarding days or months is an act of the pre-Islamic era of ignorance (Jahiliyyah). The Prophet, peace and blessings be upon him, said: "Superstitious omens are shirk (polytheism), superstitious omens are shirk." Therefore, a person should rely on Allah and depend on Him in all their affairs. You should gently advise your mother and correct the misconceptions she holds regarding this issue.