The question as stated is a little broad, but I will try to point to some Biblical bases for using extra-Biblical sources to aid the common Christian endeavor to follow Christ.
I am answering from the perspective of my Catholic faith, so perhaps I would not whole-heartedly assent to an unstated assumption in the question as stated, that all beliefs need a Biblical basis in order to be valid. A Catholic would also assent to the two other sources of Tradition, loosely defined as the oral teaching of the Apostles as expressed in the unanimous consent of the Church Fathers, and Magisterium, which serves as arbiter between conflicting interpretations of Scripture and Tradition. Given this brief caveat, I will try to confine myself to Scripture to show the reasonableness of using extra-Biblical sources.
Consider the very last verse of the four Gospels, Jn 21:25:
But there are also many other things which Jesus did; were every one of them to be written, I suppose that the world itself could not contain the books that would be written.
We have a Biblical example of this in Acts, when Paul says to the Ephesian elders (Acts 20:35)
In all things I have shown you that by so toiling one must help the weak, remembering the words of the Lord Jesus, how he said, ‘It is more blessed to give than to receive.’”
Where did Paul hear these words? Evidently, from one of the Apostles. Granted that Acts is now part of the Canon and not "extra-Biblical"--though I would caution that it is naive to ignore the human process by which the sayings and deeds contained in Scripture were gathered and redacted--this example still sheds light on the broader question: why read anything outside of Scripture?
St. Paul recommends the reading of Scripture (Col 4:16):
And when this letter has been read among you, have it also read in the church of the Laodiceans; and see that you also read the letter from Laodicea.
...but it is curious that his most often repeated words of counsel are similar to 1 Cor 11:1:
Be you followers of me, even as I also am of Christ.
and (Heb 10:24):
And let us consider how to stir up one another to love and good works.
These last two recommendations involve imitating a person or speaking with words--words which in no way are "Biblical". If Paul encourages me to exhort my brother in the Faith, is it no surprise that ever since then Christians have used the mouth and the pen to exhort their brothers? The epistles of Ignatius, Clement, and Barnabas are some of the earliest examples. Clement, for example, is firmly conscious of this office of "admonishing" when he writes in c. VII:
These things, beloved, we write unto you, not merely to admonish you of your duty, but also to remind ourselves.
"Admonishing" is an extremely "Biblical" action, though it involves our own words. Though we have many records of the words that Paul or Peter used to preach to the crowds, how many times are we simply told that they "preached" and "converted many"? Those words were certainly extra-Biblical.
In the end, the point is ridiculously simple. Christian books are the attempts (some great, some mediocre, some bad) of Christians to fulfill this Pauline precept of "exhorting" their brothers and Christ's command to "preach as you go, saying, ‘The kingdom of heaven is at hand.’" (Matt 10:7) There is no formal difference between preaching by word and preaching by pen. If I can listen to a homily, why can't I read a book? I personally have enjoyed many of the radio broadcasts and books of the Archbishop Fulton Sheen, though I never listened to him in person.
Should we use any source other than the 'one source'?" Of course. Just as I look up on a map to see where Cana is, or read scholarly sources to see what Sadducees believed, or read the Bible in translation (=interpretation), so I will go to people I have good reason to trust--both living and dead--to seek guidance in following Christ, whether it be by word, letter, radio, or book. The "one source" never suggests that is is the "only source."
