Is it permissible to teach bicycle riding to girls who do not adhere to Islamic dress and manners, taking into consideration that teaching them to ride may lead to open temptation?

If this activity leads to unlawful acts (munkarat shar'iyyah) on the part of most of the women engaging in it, who are not committed to Islamic dress (al-ziyy al-shar'i) and Islamic manners, then it is not permissible for you to teach them. This is due to the temptation (fitnah) and unlawful acts present during the teaching, and the assistance provided to such acts thereafter.