Use the adverb shyly when someone acts in a timid or fearful way. The new kid at school may hesitate before shyly asking if he can sit at a busy cafeteria table.
If you're reserved and self-conscious, it's natural to behave shyly at social gatherings. You might stand shyly to the side, too timid to join a conversation, or shyly slip out early without telling anyone you're leaving. Shyly and shy have a Germanic root that means "afraid." Even shy people can be brave, though, like when a child shyly invites a new friend to play after school.