You cannot conclude anything about biases based on a single answer. But if there are 100 answers and you mark "I am [better] than the average*" in 90 of them, it is likely that there is some bias present. It could be
that you would really be better than average* in 90 of 100 cases, but it is highly improbable. If you answer "above average" in 40 questions, "below average" in 30 and "about average" in 30 (or similar numbers), that is more realistic.
*I think it should be the median here, where exactly 50% are better by definition.
But not everywhere at the same time.
This requires to have questions about many different areas, of course. If you compare yourself to all others in 100 questions about your work, 100 times "above average" is not surprising.
By the way: If you know that the test evaluates your bias, your answers will be biased, too, of course, which would make a nice meta-study ;).