A friend tricked me into watching a few episodes of the show, so I'll chime in.
Bones herself strongly fits a textbook MBTI definition of a sensor. She lives and thrives in the world of what are (at least in her view) objective facts. She doesn't put up with much nuance or unfounded speculation. As a rule she sticks to things as they are. While one may argue that this comes from her scientific background, the behavior is prototypical S.
Given this noticeable S, I would propose that the character leads with her S function, suggesting either IS_J or ES_P. Of those two, I feel that IS_J is considerably more reasonable because she has shown to not be inherently "experience seeking" as one may expect from one leading with Se and because she deals heavily with the past both as her occupation and in her occupation. (the latter by connecting details she recalls from previous instances, suggesting an Si-like memory)
From there, it's ISTJ or ISFJ. She seeks to deal with the world objectively (from a standpoint of definitions, T>F) and with strong regards to empiricism. (Te>Ti)
While she does not always appear to meet the often negative SJ stereotype, Bones fits the ISTJ profile almost perfectly.
Because I'm lazy, I'm just throwing out ExFJ for Booth. Strong focus on people and drawing out emotions.