There may never be a clear winner in the nature/nurture debate. Most psychologists now opt for an interplay between the two and timidity is no exception.
In terms of nature, studies of identical twins point to a correlation between heredity and anxiety-related disorders. Experiments have also shown that young babies react differently to stimulation. When shown a brightly colored bouncing mobile, some reach out for it, some watch passively and while others shy away. Some have estimated that as much as 40-60% of anxiety problems could have genetic roots.
This suggests that there are at least some physiological mechanisms at work. People differ, for example, in how their systems produce and regulate brain chemicals, such as the neurotransmitter dopamine, which can influence how pleasurable we find novelty. Individuals also differ in their sensitivity to perceptual information. What might be pleasing to somebody with average hearing and musical sense, for example, could be jarring to someone with highly acute hearing and perfect pitch.
Many psychologists prefer to describe of genetic factors as a "predisposition" rather than an indelible fate. This is to say that some people may be more vulnerable to feelings of anxiety or inhibition than others, but it's not a foregone conclusion.
Nurture can influence the extent to which natural tendencies are expressed. People who are prone to over-cautiousness can be given strategies to manage and even overcome it. Over time, positive experiences with new situations can help someone override their initial misgivings. They may continue to feel a few pangs of anxiety when faced with something unfamiliar but do not necessarily shy away from it.
Environmental factors and life experiences can also create timid behaviors. A child whose been bullied or abused, or suffered a serious illness may develop an understandable caution about diving straight into unknown waters. At home, anxious parents can inadvertently send messages through their own worrying that the world is full of dangers the child should try to avoid. Even in adulthood traumatic events can induce timid-like behaviors. Two common symptoms of post-traumatic stress are an increase in avoidance and a more sensitive startle response. Someone unaware of the sufferer's condition might assume they are meeting a timid person.
Perhaps the most important point about being timid, however, is that describes how someone acts, not how they feel. Physical differences might account for how each of us experiences novel sensations and we naturally want to avoid what feels unpleasant. Psychological experiences teach us that new situations can harbor unforeseen dangers and we'd prefer to keep a safe distance. Whether we choose to act on these impulses is another story.