In the 19th century and early 20th century the bicycle was a popular and viable method for serious transportation. The mechanisms are simple and relatively easy to repair compared to the emerging automobile, while being very affordable. A horse was out of the question for many because of the constant maintenance, for instance. A group of women brought photographic equipment with them and rode halfway across the American continent.
Even the old "Swiftwalker", made by a German builder out of wood, was almost as fast as a horse for long-distance travel. It was a wooden beam with two wheels and a seat, but without pedals. One used legs and feet to propel it, and then coasted with feet up off the ground.
If the bicycle were reverse-engineered, even without the intricacies of the chain-and-sprocket mechanism, it could revolutionize travel in that world.