This question seems just weird to me. How do you know you can trust your cognitive system that says "nah, I'm not being biased right now"?

It's weird to me that the question is weird to you X-/

You know when and to what degree you can trust your cognitive system in the usual way: you look at what it tells you and test it against the reality. In this particular case you check whether later, more complete evaluations corroborate your initial perception or there is a persistent bias.

If you can't trust your cognitive system then you get all tangled up in self-referential loops and really have no basis on which to decide by how much to correct your thinking or even which corrections to apply.