The only person in the bible who has secular proof of existence (that I know of) is Pontius Pilate. His name is recorded in Roman records as a government official.<quoted text>
They became believers because of what they witnessed, and because they wanted to preserve it, they wrote it down. First century Israeli culture was an orally dominated culture. Historical event was memorized and passed on within specific communities and groups. Look it up. Not only that, they were what is known as a "high context culture." Many things were left unsaid (or unwritten) because the assumption of the culture was that if you were a part of that culture, you knew what everybody else in that culture knew. It didn't have to be defined or discussed in detail.
If you're trying to imply that their bias fed into their beliefs, then you would be partially correct, but not in the way that you as a skeptic might think. The bias of the early Christians (the apostles specifically) existed because of what they witnessed with their own eyes, and grew in proportion to their faith. Your implication that believers words don't count because they're believers also fails in another way.
This history mattered to them because they saw it as sacred and holy. It wasn't a matter of discussing why their camel or donkey was getting old. This was a big deal to them, so of course they had bias. Would you expect a passionate sound engineer to write a 50 page doctoral thesis on the subject of Victorian era plumbing and sanitation? You have bias, I have bias, everybody has bias. Your unstated (yet implied) charge isn't a logical argument.
The Romans did not have a religious drum to beat. The records do not say anything else about him, whether he pronounced judgement on a man named Jesus or even whether or not he had a wife who might or might not have a had a dream.
Again, do you have any independent, secular proof? We've all heard fish stories.....and the one that got away keeps growing. That's pretty much an example of oral history.