Religious identification is very subjective and I think it should be up to each individual person if and how he or she wishes to be classified.
Sure, here are certain labels like various denominations-- "Catholic," "Jehovah's Witness," etc.-- which have more specific connotations because they involve a certain institution and a definition of orthodoxy and orthopraxis which, while it may have some leniency, generally rules out more than it rules in. To give a silly example, I think it would be a contradiction in terms to say that you are Catholic but you believe that Al Gore is the head of the church and the embodiment of God on earth. Sort of like saying that you're a cat except that you walk on two legs, don't have hair, speak English and are descended from human beings... the word just loses all meaning
But a broader terms like "Christian" (or for that matter "Pagan," "Buddhist," etc.) has so many different definitions varying through time and space that I think it's fair to say that if you feel like the label fits you, then it probably does. Many people base their religious ideas off of the Bible but have completely different interpretations, ranging from the fundamentalist to the entirely metaphorical. I don't see that anyone has a right to tell you that because you appreciate the message of Jesus but not the more literal Bible stories, you have the "wrong" way of relating to the Bible, you can't call yourself Christian.
If you don't already know about it you might consider looking into Unity church if you're interested in finding other people with similar ideas. They use Christian terminology but seem to focus on the moral philosophy and allow for a great deal of personal differences and subjective interpretations among their members. I am not anything like Christian myself, but the Unity people are interesting and usually very kind and open minded.