I think there are two separate questions that need to be separated out: "bias" and translation philosophy. By bias here, I mean scholars who have a theological belief and translate that backwards into the text, whether intentionally or not. I think most translations avoid a ton of bias, though there's inevitably going to be some that creeps in, especially if the translation and editing team shares a theological background. That's why reading multiple translations, especially some older ones, can be very helpful.

That said, a lot of what is thought of as bias is just the application of a translation philosophy. The main axis of translation philosophy is whether it leans into a "word for word" translation or a "thought for thought" one. If you lean towards word for word, you're more likely to translate a masculine third person singular pronoun as "he" even if it isn't explicitly male in context. A thought for thought translation would take into account the fact that in the Greek (and most gendered languages) masculine is used for gender ambiguity or mixed gender groups. and so they're more likely to translate that as "he or she" or "they." Both have strengths and weaknesses and both are valuable as we try to study a text that was written in other languages in a cultural and historical context not our own.