It would seem to me, that if you want to know Jesus, and understand Jesus more than ever before, so long as Jesus exists and can communicate with you, you can do such a thing. Arguably, believing or disbelieving the Bible would have little to nothing to do with this. Unless Jesus brought up the Bible, and wanted to use it with you. Also, arguably, being a "Christian" might have little to nothing to do with whether or not you personally know Jesus and could become like one of Jesus' disciples.
If you are going to rely on what was written about Jesus, or what others say about Jesus, and not on Jesus directly ... then I'm not sure what that would be called. Probably some form of Christian or Christianity, although other religious traditions include Jesus in their tradition as well obviously. I don't see how you could really know about Jesus otherwise apart from someone telling you in such a context. This may involve referencing books, obviously. I would think if you wanted to know as much about Jesus as possible from this method, you would probably reference as much material as you could. Which opens up a LOT of reading, obviously even outside of a "Christian umbrella".
If you wanted to combine all of it ... if you were able to know Jesus personally as well as reference others and other materials, I would think Jesus Himself may be able to tell you what is what concerning what to believe or disbelieve about what was said in books. However I suppose you could still choose to believe a variety of things, even if told otherwise.