Since the New Testament writers were biased, can we trust their testimony?

Yes, we can trust their testimony. Being biased about something does not mean that you cannot tell the truth. Take for example the case of a robbery of a small store. The robber shoots and the wounds two employees, escapes, but is later apprehended. At the trial the employees who have recovered from their injuries are brought in to testify. Both of these witnesses are biased in that they want to see the perpetrator properly punished. But, under oath their testimony is accepted as perfectly valid -- providing there aren't obvious problems. So, being biased does not automatically mean that the testimony they give is not true.
The New Testament writers were certainly biased, but their bias was towards honesty and truth, not deceit. Their intention was to accurately record and testify to the events that they had seen. Remember, the disciples were followers of Jesus who taught them to love, to be kind, faithful, and honest. And this wasn't all. Jesus warned against hypocrisy (Matt. 6:1, and against bearing false witness (Matt. 19:18 ). The whole life of Jesus was based on integrity, character, faithfulness, truthfulness, love, and sacrifice. This is what the disciples learned from Jesus and this is what they taught in their writings. So, if they learned anything from Jesus it was to live in truth for this is exactly what Jesus said, "Sanctify them in the truth; Thy word is truth. ¹⁸ "As Thou didst send Me into the world, I also have sent them into the world. ¹⁹ "And for their sakes I sanctify Myself, that they themselves also may be sanctified in truth," (John 17:17 -19).
Furthermore, the fact is that there were plenty of people around who could have discounted what the apostles had written if what they wrote was inaccurate. Yet, we find no evidence of any such thing in any writings of the time. Yes, the disciple were biased. But to what? To lying? To exaggerating? Or were they biased towards the truth of who Jesus is and what He had done?
Of course, just because eyewitnesses wrote about Jesus rising from the dead does not mean it actually happened. This is true, but why would the disciples lie about this? Why would they risk the lives, their families, their cultural ties, and even end up dying for it all if they knew it was all a lie developed out of their "bias"? It doesn't make sense. But what does make sense is that the disciples were telling the truth.