The art of history is that of using all the knowledge you have, and making logical conclusions based on primary sources. The only way to accurately determine what happened in the past is to get as many different sources as you can, and put them together like a puzzle. Each piece on its own has some truth in it, so that all the pieces together make the whole truth. When doing this, you have to take into account the bias that a particular source may have.
For example, Emperor Valerian of Rome, is said to have been captured in battle by the Sassanids. The Roman Record says that he had been captured in battle and no one ever paid his ransom. On the other hand, the Persian record states that Valerian was killed in a battle that is not found on the Roman record.
A previous emperor, Decius, also died in battle with the Goths. So you have to think, maybe the Romans were disgraced by losing their second emperor in a very short time, so they used propaganda to cover it up (Mike Duncan, The History of Rome).
When attempting to sift through historical bias, you have to take into account all of the factors that influenced the writers, and then you can get a fairly accurate picture of what happened, maybe with a few puzzle pieces missing. Unfortunately, the only fail proof way to find out the truth would be to go back in time.