Bullying only occurs when a person is in a situation where they cannot defend themselves .... stating facts about a person is not a case of bullying.
Young people in school do experience bullying and can be both physically and mentally abused because they do not have the life experience, physical size and other factors to defend themselves. Mentally, disable people can also be easily bullied. Physically, challenged can also be easily bullied.
Someone writing a letter to a public figure who is old enough and smart enough to defend herself and to know that being in the public eye she is going to open herself up to criticism (whether that be her speech, dress, looks or weight) and telling her that she is fat and should do something about her weight, is not a case of bullying.