Can an Orthodox frum woman who keeps tziniut ride a motorcycle? If yes, then what type of clothes should she wear to keep her tzniut (knees covered with skirt).
A quick search through the Internet shows, as expected, a disagreement among Poskim.
Rav Eyal Karim, Rav Amos Sherki, and likely Rav Yaakov Ariel (he is asked a slightly different question) say that it is allowed. Presumably, one would need to keep the same standard of Tzenius that they always adhere to.
Rav Meyers notes his own (slightly better sourced) Teshuva about riding bicycles found here. Various Poskim have ruled on that Shaila as well, see Rav Aviner's Heter and kipa.co.il's answer, which has a wealth of online links. See Are women allowed to ride bicycles for transport? as well. (H/t to DoubleAA for making this connection.) Also related to: Are women allowed to drive?