Hi Kait, is it really your Grandmother born 1877? That would make you quite special.
Looking through the British Newspaper Archive, it's interesting to see just how embedded the cycling phenomenon was by 1891, a search on that year alone for "cyclist" produces some 727 pages of hits. A lot of the hits relate to cyclist clubs and their activities, such as meetings and tours. However, it doesn't take too much of a leap of faith to imagine that some saw the delivery / messenger opportunities associated with bicycles back then.
So, were your grandmother and her brother actually employed using their bicycles back then, say, as delivery messengers for a shop? Possibly, but I don't know. Or was it a humorous reference to a couple of cycling crazy children?
What is clear is that the penny dropped on the business benefits of the bicycle in the late 1890s, for there are newspaper articles announcing the introduction of cyclists into the GPO with predictions that this would pretty well revolutionise the telegraph.