Hmm, if I say that I’m lousy at being objective, wouldn’t that in itself be an instance of objectivity? In which case, am I really lousy at being objective?
If I say I’m good at being objective, isn’t that what I would likely think if I were actually bad at being objective?
The best answer I can give is that I’ve done enough reading of research to know that we’re all blind to our own biases. At best, we can recognize that we’ll continue to fall into the same fallacies over and over, without seeing that we’re doing it. Even the folks who study these biases aren’t immune to them. So yeah, sure, I’m marvelously objective.
By the way, since you mention tests, a well-designed psychological test (e.g. personality test) will take into account the subject’s unreliable objectivity. There are many mechanisms test designers use to get around this.