Ususally what many of these opposers apparently mean by "doctrinally biased" is that the NWT translates passages that may have more than one possible interpretation in a way that does not support the trinity doctrine (or certain other "orthodox" doctrines of modern Christendom). Just because they support some of these doctrines (particularly the trinity doctrine) does not make them true. Jehovah's Witnesses have determined through proper, honest scholarship that a number of these teachings are actually unscriptural additions by scholars and philosophers made hundreds of years after the deaths of Christ and his Apostles. - See the HIST; CREEDS; ISRAEL; IMAGE; etc. study papers.
For Jehovah's Witnesses to choose honest alternate translations and interpretations which refute these unscriptural doctrinal additions or questionable translations may make them biased, in a sense, but it certainly does not make them dishonest or guilty of "faulty translations"!
Being "biased" does not necessarily make a person dishonest or unscholarly. Being biased against illegal drug usage and drug pushers does not make you a villain. Being biased against abortion or biased against having children out of wedlock or adultery, etc., does not automatically make you wrong, dishonest, unscholarly, or evil! We are all biased in many ways and often in good, proper ways.
All Bibles are doctrinally biased in their translations. For example, it is doubtful that you will easily find one for sale today which is not strongly biased toward a trinity doctrine. That is, when more than one honest rendering exists for a particular verse, these Bibles will purposely choose the one which best presents evidence for a trinity. This is solely because of the tradition of a three-persons-in-one-God trinity doctrine which was officially begun by the Roman Catholic Church in the 4th century A. D. (hundreds of years after the deaths of Christ, his Apostles, and the inspired Bible writers) and continues down to today in 99% of the churches of Christendom.
This trinitarian doctrinal bias is not based on proper Scriptural evidence (see the IMAGE; PRIMER; I-AM; etc. study papers). It is not based on proper historical evidence (see ISRAEL; HIST; and CREEDS study papers). It is not just "doctrinal bias," it is unsupported doctrinal bias.
So for the NWT to be virtually the only Bible to be consistently translated with its properly-supported bias for a single-person God is certainly not dishonest or false!
Additional Reading:
Is The New World Translation Biased and Unscholarly? (In Defense of the NWT)
Robert Hommel's Comments on the New World Translation (Bible Translation and Study)
Index of Links and Pages that Defend the New World Translation (Defending the NWT)