In Ancient and medieval times It seems they had all the materials to make a basic bicycle (metal, chains, wood) except perhaps rubber but I think wooden or even leather could still make a decent replacement.
Why didnt they have "bicycles" in those time periods and who came up and used the first bicycles?
The device most often identified as the original proto-bicycle, the "draisine", was invented by Karl von Drais in 1817. It was essentially a bicycle without pedals, made out of wood. Because it was kick-propelled, rather than with pedals, some people do not accept von Drais "velocipede" as a proper bicycle. One thing to note however, is that von Drais' invention did feature a steerable front wheel, which is essential to make a bicycle ridable. With regards to why nobody thought of it earlier: ideas that seem simple in hindsight are often overlooked for a long time. In addition, the idea that it is possible to balance oneself on two wheels is not obvious at all.
The draisine did not receive very wide acceptance, but it was quickly followed by a number of imitations and minor improvements. A notable one was sort of kick-powered draisine with an additional hand crank to provide extra power, invented by Gompertz in the 1820s. It would take until the 1860s before the pedal powered "velocipede" was introduced by Michaux and Lallement.
You mention rubber; the introduction of pneumatic tires was actually an important step in making bicycles a practical and safe means of transportation over longer distances.
As for human powered transportation devices in general, the idea has been around for a long time. (Inline) skates were invented in the 18th century by John-Joseph Merlin, and ice skating is much older. Some people have suggested that von Drais himself might have been inspired by ice skates in designing his proto-bicycle. The reason it is possible to skate smoothly is that you can constantly correct the position your body's center of mass by moving forward: it is much easier to skate on one skate than to stand on one blade. The same principle applies to the bicycle balancing on two wheels. Off the ground, Da Vinci sketched a number of human-powered vehicles, including his famous aerial screw and a type of pedalo, and of course (paddle-powered) canoes date back to pre-history.
References include Herlihy, Bicycle, The History, Hadland and Lessing, Bicycle Design - An Illustrated History and Wilson, Bicycle Science.
