BA and MA in World History here. Historians have dealt with this issue since events began to be written down. Even with semi-verifiable sources, resources from let's use your example from the time of Jesus are hard to taken with certainty. The meaning behind the word mythologized is based on the root word myth which means "a widely held but false idea or belief". This helps you answer your question. Historians are often taught to gather several different resources: biased/unbiased/primary and secondary and sift through those to ascertain an idea that can be verifiable, without this ability to verify your end piece will be nothing than a basic narrative. A great example of this is reading Herodotus, and then reading anything past Hegal, where history became more "scientific". But to more exactly answer your question. If you can find, more than two different resources that can state, "Jesus was here on this date and did this" you can ascertain that there is more validity in that event than finding only one resource that states the same.

I would add that often modern historians are interested in the 'myth' as much as the 'fact'. Since history has become more interested in culture there has been greater interest in unpacking the cultural elements preserved in historical sources. From that point of view the myth is less problematic since its existence is a historical fact even if its content may never have occurred.

As to the bible, it is important to remember the bible is not one source, but many sources, and sources that are internally conflictive at times. For example, Kings and Chronicles cover much of the same historical material but present that in different ways. Similarly, the Gospels cover a similar sweep of time and were composed at different times.

Remember historians aren't just chroniclers, we don't just read sources, identify 'facts', and write down what happened in chronological order. We are scholars of humanity and human existence interested in studying change over time. We can study how myths change over time, or how a myth develops, or how people remember the past (surprise! they don't necessarily do that very accurately).