... A second answer.
1. Question Restatement:
Is it possible to "bracket" your bias during interpretation, enabling you to essentially approach the text in an "unbiased" manner, despite the bias that is technically present?
2. Answer - Attempting to Avoiding Bias leads to an Automation Bias:
As a "thought experiment": can a computational, philological, computing system be created that can interpret any text - let alone a Biblical text - without any bias, (even Confirmation Bias)?
Confirmation Bias, Wikipedia Article: the tendency to search for, interpret, favor, and recall information in a way that confirms one's preexisting beliefs or hypotheses. It is a type of cognitive bias and a systematic error of inductive reasoning.
Human cognition, by definition, necessarily requires an act of associating an inquiry with prior experience and knowledge, (also see constructivism theory).
This means that any absence of experience, or knowledge, will always cause that examination to be biased - towards previous experiences, and attained knowledge - notwithstanding "divine revelation" and "noetics".
Even when modeling artificial intelligence, some form of cognitive bias is always present - and some biases are necessary conditions for learning.
Specifically, if one were to go to the extreme, to try to "bracket" all possible biases, (perhaps to the extent of using a computer simulation) - it would still, necessarily, lead to an "automation / computation bias".
Automation Bias: The tendency to depend excessively on automated systems which can lead to erroneous automated information overriding correct decisions.
Bracketing Bias: The tendency to depend excessively on unbiased, computated, conclusions which can lead to erroneous inferences overriding correct conclusions, (yep, just made this up; apropos, the existence of "God" is a perfect example of this - another discussion).
In other words, it is impossible to avoid all biases, and therefore necessary to determine which forms of biases are actually valued in Biblical hermeneutics, (a computational / deductive bias is certainly not one of them).