According to Merriam Webster Dictionary, “The quality of not being too proud or confident about yourself or your abilities is modesty”.
A woman covers herself so that a man should know her for her mind, not her body and that is what the purpose of Hijab.
Definitely, modesty without Hijab is possible. Consider the famous Malala Yousafzai, a Pakistani activist for female education and the youngest Nobel Prize laureate. She would have been the same even without wearing Hijab. It is the deeds that decide, how a person is! If one is humble and not haughty, that person remains the same even in front of the elders or younger people.
In Islam, men have an obligation to God and to women to observe hijab. Nonetheless, someone who doesn’t wear a hijab is not any less a Muslim than someone who wears it. Hence, it is high time we get rid of this bias and move on and learn to accept people for their noble deeds and good work rather than judging by how they look.