According to Wikipedia, Belief bias is
An effect where someone's evaluation of the logical strength of an argument is biased by the believability of the conclusion.
Basically, your own beliefs, prior knowledge, etc., affects your reasoning process.
There are three types of factors that influence belief bias: time, nature of content, and instructions given.
You are more likely to have belief bias if you have less time to evaluate an argument, negative emotion prompts, and less instruction.
So what can you do to be aware of it?
According to Changingminds.org
When you are listening to arguments of others, think not only whether something 'makes sense' - think also with a cold logic as to whether it is possible or true.
This is extremely hard to do due to my line of work where my role is evaluate companies and founders to make an investment. All sorts of biases comes up when you are listening to founders vision (especially on a phone call) but I am aware of the bias.
One of the things I do is ask in-depth question if it's something I am "skeptical" or if it doesn't "make sense" to understand their reasoning. Then I do my own research and try to learn moreabout it.