How to avoid subtle biases and inclinations to influence phenomena when doing vipassana? In other words, how do I know if I'm really being objective?
Find out the difference between what are concepts and what is. 

Follow the sensation of the breath not the idea of the breath. 

Follow the sensation of the feet as they move exactly in the present moment and don't follow the idea of the feet.

Notice thoughts as they happen or as they are remembered but don't make an effort to notice or not notice the content of the thoughts.

Notice what mental content is being reacted to, notice intentions. 

When you merely witness what is in attention and realize that it is what it is then there cannot be any bias in that moment. Bias comes with consepts.