Shy, bashful, diffident, modest, coy can mean showing disinclination to obtrude oneself in the presence or company of others.
Shy implies a shrinking, sometimes constitutional, sometimes the result of inexperience, from familiarity or contact with others; shyness usually manifests itself in a certain reserve of manner or in timidity in approaching others.
Bashful implies an instinctive or constitutional shrinking from public notice that usually expresses itself in awkwardness of demeanor and is especially characteristic of childhood and adolescence; as applied to mature persons it connotes abnormal or excessive shyness and lack of savoir faire.
Diffident implies a distrust, which may or may not be warranted, of one’s own ability, opinions, or powers that gives rise to hesitation in their exercise.
Modest, without implying self-distrust, may denote an absence of all undue confidence in oneself or one’s powers, but often it stresses not an inner lack of confidence but a manner free from brashness, boldness, and self-assertiveness.
Coy suggests assumed or affected shyness, often with the further implication of coquetry.