While it is clear that J.R.R. Tolkien did not write The Hobbit solely as a Christian tale with biblical application around every turn, there are several overarching concepts in the novel which are also consistent biblical concepts.
The first and most obvious biblical concept found in this novel is the battle between good and evil. It is the central conflict in the story, and there is very little doubt about which side the characters and creatures are on; when there is any doubt, it is the characters who struggle to discern the truth--like Eve does with the serpent. Evil is constantly nipping at the heels of the travelers and preying on the innocent towns and those who stray too far away from civilization. Satan, too, is described as a roaring lion, seeking whom he may devour (I Peter 5:8).
It is true in this novel that good people are capable of doing bad things, but that is also a biblical principle; in the Garden of Eden, Adam and Eve lived in a perfect world but they sinned, and from then on man has to do constant battle against his tendency to sin. At the end of the journey, however, good triumphs over evil, which is another reality found in the Bible.
A second example of biblical principles being infused into The Hobbit is the fact that Gandalf uses someone who seems quite unsuitable to accomplish a great task. Bilbo is only a little hobbit who thinks he has nothing to offer (and others certainly agree with him about that), but Gandalf sees something in Bilbo which he can use. Compare that to the unlikely characters in the Bible who were chosen by God to accomplish great things in His name.
David, a young boy with a sling, defeats a great giant named Goliath. A small boy with a few loaves of bread and several fishes offers what he has, and Jesus uses it to feed five thousand or more--with leftovers. A prostitute named Rahab protected God's men from their enemies at the risk of her own life, and a young Jewish girl named Esther became a queen and saved her people from death. Just as God saw something in each of these characters which allowed them to be used to do mighty things for His glory, so Gandalf recognized some qualities in Bilbo which he knew could be used to ensure a successful journey.
Finally, the theme of destiny (which can also be called fate or a plan) versus chance is another point of comparison between the novel and the Bible. The Bible is full of reminders that God has a plan for each person, as in Jeremiah 29:11:
"For I know the plans I have for you,” declares the Lord, “plans to prosper you and not to harm you, plans to give you hope and a future."
Gandalf reminds Bilbo that what they encountered and how they were victorious on this journey were not mere happenstances or accidents of chance:
Surely you don't disbelieve the prophecies, because you had a hand in bringing them about yourself? You don't really suppose, do you, that all your adventures and escapes were managed by mere luck, just for your sole benefit?
While The Hobbit cannot be read as a complete reflection or an accurate accounting of the Bible, there are certainly biblical themes present in the Tolkien's work.