Does everybody have a bias?
It's more accurate to say that everyone, without exception, has biases. From the WP article on bias:
Bias is disproportionate weight in favor of or against an idea or thing, usually in a way that is closed-minded, prejudicial, or unfair.
Let's start with your last question:
Otherwise, with the opinions of others, is there any proof to 'Everyone has a bias' as being completely true or wrong.
Science, by way of biology, is very clear on this matter: yes, evolution dictates that people are born with biases, perhaps the most powerful to favor survival. Human thought generally speaking is disproportionately weighted in favor of survival and reproduction in a way that is close-minded. Because of this drive to survive and replicate, the brain has a host of biases towards this end. Cognitive biases then are often cast in the light of being adaptive and possessing survival value. One extremely powerful argument in favor of this view is Thinking, Fast and Slow by Daniel Kahneman who received a Nobel Prize for his work in the psychology of bias. One of the central premises of the book is that we have two general systems of thought, one slow and rational, and the other fast and stereotypical, and that the latter is about survival value. In situations where the latter is used, it has a powerful capacity to undermine rational thought.
One important dimension of where our inborn sense of bias comes into play is reasoning about in-groups and out-groups, which is a function of our evolution. Evolutionary psychology is a branch of biology and psychology that offers support that our reasoning capacity functions somewhat at the mercy of emotions, and there is research by Antonio Damasio that supports the idea that emotions guide bias and the use of logic.
To say 'all have a bias' is to then say that I have a bias. If I have a bias, then I was either given a bias, or I had taken up a bias. For, to have something must mean I was given that something or I had taken that something.
Yes, you too are born with thinking, fast and slow, and have biases.
So, I could then say that the statement 'everyone has a bias', the arrangement of the simple sentence is wrong? would it be more useful to say 'everyone has the capacity to have and not have a bias'? as a bias is something that is conditioned not predetermined as a cause of being born? Or, is the effect being the bias a thing that derives from the cause, which is birth. which is then to say that 'everyone has a bias' is correct.
The cause of bias, in some indirect sense, is to be in possession of a brain wired to value survival and reproduction. One particularly common and powerful bias, then, is the disposition towards naive realism which is a cognitive bias that predisposes people to adopt the philosophical stance of naive realism. Biases, then affect our metaphysical presuppositions, and those metaphysical presupposition determine to an extent our logical discourse. The question of 'who is human', for instance, varies greatly in history, with one group of people often exterminating another. The Armenian Genocide is a classic example of how in-group/out-group biases can affect how whole societies reason about who deserves to live and die.
In cognitive science, it is generally accepted that the extremely rational is the exception and not the rule, and that logical fallacies are largely inspired by cognitive biases. Belief bias is a evidence-based position that all of belief and reason in general is biased in favor of the individual, and that rational intelligence is but one aspect of thinking and is influenced heavily by irrationality. This is a position that has been held by a number of contemporary proponents including Daniel Goleman, Howard Gardner, Dan Ariely, George Lakoff, and Steven Pinker, but has been a theme by many great philosophers famously Thomas Hobbes.
[I]s there any proof to 'Everyone has a bias' as being completely true or wrong.
For those of us who relish in logic, reason, argumentation, and philosophy, the fact is that human beings are overwhelmingly predisposed to struggle with fallacy inspired by bias. The shift from Homo economicus to a more nuanced view of humans as fallibly reasoning creatures is almost entirely based on evidence that bias is a substantial and universal force in argumentation and reasoning.