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?
It is possible to "bracket" a subset of your bias but not all of it.
As an analogy, if you do not like the look of a certain food you can agree to take a blind taste test to find out whether you like the taste, knowing that you wouldn't be able to escape your bias against the visual appearance of the food if you were not blindfold.
However, the philosophical question becomes much more, well, philosophical, when you start talking about setting aside your framework or worldview. The problem is that we are now talking about issues at the deepest level of our understanding, and they encompass the very action we are trying to undertake. Consider this question: what is the meaning of 'biased' or 'unbiased'? Does not the answer depend on your worldview? A postmodernpostmodern might believe there is ultimately no such thing. Everyone else will have their own perspective.
Logically, you cannot set aside all your most foundational beliefs. This is because all your decisions are ultimately based on these foundations, including your decision to try and set them aside. In other words setting them aside would also involve setting aside your decision to set them aside: a logical nonsense.
So, can we "bracket" your bias during interpretation?
The question is unanswerable unless you define the domain in which you are trying to set aside bias. Once you have defined 'bias' in the domain in question you can seek to set it aside, but trying to be wholly objective is impossible: just framework-blindness by another name.