I carry open while riding my bike throughout the state as many others do. You need a license for vehicle carry as the license is for...in a vehicle or concealed on your person. A motorcycle is defined as a vehicle in the law. The license used to be for "concealed in a vehicle or on your person" but this changed with the Montgomery bus boycott in 1956. Boycotters in carpools started open carrying guns in a vehicle (legal at the time) to stop the police from harassing them. The law was changed to make it illegal for them to carry in a vehicle without a license.
As a history note, all of Alabama's licensed carry is due to racism. Concealed carry was against the law to stop Indians, slaves and abolitionists from hiding guns. Concealed carry licenses were then set as "may issue" by the sheriff's so they pick and choose who to give them to (meaning whites only). The concealed carry license was changed in response to the bus boycotts which lead to a loss of revenue for the city. That is why the carpoolers and others were harassed by police to get back on the buses and why they started arming themselves while in cars.