Fatwa dari laman islamweb.net
In principle, it is permissible for the woman to practice the sports of cycling, horse-riding or running if the Sharee‘ah criteria are met. Doing these activities before non-Mahram men most likely leads to violation of Sharee‘ah rulings, as previously clarified in Fatwa 87602. We do not know how you understood that what you mention is the main reason for preventing women from riding bicycles. In fact, there is no analogy between the two cases. That is because when the woman rides a bicycle, she makes some movements and actions which may cause her to fall into religious prohibition.
In fact, your husband was right when he told you that a woman is not allowed to do these sports in front of non-Mahram men due to the evil consequences we mentioned above. Moreover, the race that was between the Prophet , and his wife ‘Aa’ishah may Allaah be pleased with her did not take place in the presence of the Companions. ‘Aa’ishah may Allaah be pleased with her said: "When I was young, before I put on weight, I went out on a journey with the Prophet . He ordered his Companions to proceed ahead of us, and after they did he told me to race with him. I won the race." [Ahmad]
Therefore, if you can do these activities in sport halls for women or in places exclusive to women or in a place where only your husband and Mahram relatives can see you, go ahead and practice these activities. Otherwise, you should apologize to your mother in a kind and gentle manner.
Allaah Knows best.
DOES ISLAM PERMITS WOMEN TO PARTICIPATE IN SPORTS?
Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Islam permits the person to enjoy oneself and profit from his free time i.e. out of work as long as he does not engage in what Allah has forbidden. Engaging in free time activities should not be to the extent of neglecting any of what Allah has prescribed, committing what He has forbidden or spending too much time on enjoyment and sports.
There should not be any mixing between males and females nor should there be any forbidden acts like drinking alcohol, listening to music or calling to commit bad acts.
On the other hand, these activities should be of some clear benefit to the person like keeping fit, doing mental exercises increasing knowledge or acquiring some new useful experiences.
So, if the sports, games, or activities meet these conditions they are lawful and may be engaged in by men or women, provided that the women are in a place where no man could see them.
Allah knows best.