A female is required to conceal the form and shape of her body to the best of her ability. That is not so when riding a horse due to the unique movement of the horse. Rasulullah (Sallallaahu Alayhi Wasallam) said, ?Allah’s curse is upon females on saddles (of horses).?
The Shar’ee prohibition for a female riding a motor-bike may be understood from the analogy of riding a horse. The situation of Dhuroorah (need) may grant a leeway. However, that is not the general situation today as modes of transport concealing the form and shape of females are well available and common.
and Allah Ta’ala Knows Best
Mufti Ebrahim Desai