Gandalf never tired of remarking that there was more to Mr. Bilbo Baggins than meets the eye. One assumes that Gandalf was alluding to his bravery, his courage and his reluctant tenacity - this may verily be the case - yet in the context of ancient Greek philosophy, it was the morality of Bilbo that won Gandalf's favour. A brief look at Plato's Republic will validate this point.
Around the fourth century B.C. - in the Gregorian rather than the Middle-earth calendar - Plato and a couple of wise old friends pondered the formation of ethics. In the midst of such pondering, Glaucon, Plato's brother, proposed that a myth would aid the philosophers in discovering the basis of morality. Glaucon recites the story of an unnamed shepherd who, after an earthquake, stumbled upon a golden ring in the midst of a tomb.
According to Glaucon, this unnamed shepherd pocketed the 'Ring of Gyges' and went about his daily duties. One would imagine that this included a great deal of shepherding. Later that day, when the unnamed man was attending the usual monthly shepherds meeting - as you do - he twisted the ring on his finger and became invisible. His shepherd mates, bemused and assuming that the shepherd had left, started talking about him as if he wasn't there and thus the shepherd realized the ring's power.
Subsequently, Glaucon explains in one laconic sentence, the shepherd seduces the Queen, murders the King and seizes the throne. The novelization of this myth, if Glaucon's account is anything to go by, wouldn't be quite as grandiose as Tolkien's tale.
Nonetheless, Glaucon argues that this short story demonstrates that there is no being that 'would have such iron strength of will as to stick to what is right.' Therefore, morality, according to Glaucon, is a social construct. If one would not suffer a detriment to one's reputation - through getting caught and punished - one would willingly act immorally. One might not sexually abuse the Queen and commit regicide in such quick succession, but one would at least steal a mate's money.
The great contrarian Socrates, who always seems to have the last word on such matters, claims that morality is not a social construct as this shepherd would be enslaved by his appetites and would thus be unhappy. Therefore, according to Socrates, the moral man would not abuse this power as there is value in doing what is right. The Ring of Gyges will tempt men to act immorally and yet the moral man would be able to resist its allure.
While Bilbo Baggins is certainly not a man - one should never assume such a horrible thing about a noble hobbit - the Socratic interpretation of Glaucon's myth can be applied here. Bilbo realizes the power of the ring and yet only uses it to the advantage of the people of Middle-earth, often at the expense of his own wellbeing. He fights huge spiders to save his mates, he enters Smaug's not-so-humble abode and, most impressively, he witnesses the avarice of Thorin and his band of Drawf-brothers and acts morally even when it works against his favour.
Bilbo, unlike his younger cousin Frodo, uses the ring willy-nilly, yet only to do what is morally right - and occasionally what is comical. Frodo rarely uses the ring and when he does it's often for purposes of self-preservation. Therefore, in terms of Platonic conceptions of morality, Bilbo was a greater hobbit than Frodo. This might seem like a controversial statement, yet it is one that Socrates would certainly agree with.
The One Ring, like the Ring of Gyges, had the ability to corrupt immoral beings, and only those with 'purity of heart' were able to overcome the allure of Sauron's creation. To resist temptation and to flout the impunity of social condemnation is to be a just and moral man - or in this case hobbit.
Bilbo is presented as Tolkien's hero because rather than the inexorable power that could have been gained through the use of the ring, Mr. Baggins chose instead a humble life in The Shire. He grew old with relatively little, except the knowledge that, when he was tempted - unlike those corruptible folk - he chose to do what was morally right.