Personally I do not find it to be bad manners, but probably many Japanese do as many (not all!) Japanese feel that a woman should not leave the house without make-up on and to put it on in public would be "bad manners".
Also, there are many a Japanese high school girl who, once they leave school, will, leave their school clothers in a public locker at a train station and may put on make-up in public on their way to partying with their friends. Perhaps this is why it is shunned? I do not know. Maybe others will chime in with more pertinent information.
However, like you, if I see a woman putting on make-up, or "brushing up" on a public transportation system, it does not bother me at all, but conveys to me that she wants to look her best for whomever she is meeting and therefore I overlook it. It just seems natural to me.
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