Interesting question how to tell whether you're reading a biased account. It would take an essay to answer that. After you know some history, you can tell because biases causes their owners to make mistakes. But there's probably also internal evidence too. Never seeming surprised would be a bad sign, for example.
The catch--
"History is a set of lies agreed upon" - Napoleon Bonaparte
The whole "after you know some history" demands a framework of a macrocosm to which one must depend entirely upon second-hand, at best, accounts. The glue that holds it all together is so tied to so many handles for bias both at the hands of the proxy observers as well as within the very bonding agents in the mind of the aggregator that the whole enterprise is rife with corruptive feedback potential that the anomalies that can be conclusively nailed as bona fide mistakes tend to be, for the most part, minimally useful for bias detection that tells you something you didn't already have a rather high certainty of.
wat.
Seriously, it took me something like 4 minutes to understand what you wrote there. Maybe I'm just tired.
My apologies, to all.
The key is usually to identify the larger debate going on and make sure you know the different sides. For instance if you're going to read a book by Milton Friedman it's helpful to read up on the various schools of economics to see where he fits into that debate. I believe the term that applies here is erudition. You want that.
Also, how do I know which books are most accurate? Looking at current political or biographical books, I see how slanted almost all books are because I have many other sources to go on and the relevant context to judge a book's accuracy. But all of this context is missing for historical books so I have no way of judging how biased or inaccurate they are.
What if I were learning history from the equivalent of a Glenn Beck?