I think calling her behavior "odd" is, well, odd. People are creatures of habit, and living by Mosaic Law ceremonies was a pretty ingrained pattern. It could be menstruation cleansing (pointing to the original bathing 11:2), or
Lev.5:18 Also, when a woman lies with a man, and there is an emission of semen, they shall bathe in water, and be unclean until evening
Furthermore, that was not a time and place when "forensic evidence" was people's concern. What was she going to do? Find someone to take a certain blue dress into evidence in due time?
The text note could be a further indicator that the Law was active in presence, and was functioning in a convicting way. People will do things to
mitigate their guilt, or (to placate anyone in a strong mode to deny any failure on B.'s side) even just their
feelings of guilt, and shame. Bathsheba must have felt shame, even if just for giving in to the king's advances. Women and men placed in position of powerlessness and vulnerability must cope with the aftereffects of their experiences.
Honestly, today one of the big obstacles to right interpretation is that western culture (even the church within it) has lost ALL sense of shame. There are passages of Scripture (I think this is one of them) that are greatly misunderstood because we assume those ancient people, living in an honor/shame culture quite unlike ours, acted out a mindset based on the modern conception of rights-culture.
A man or woman could be caught in a situation that brought
shame on them, and there was nothing he or she could do to avoid it; just deal with it, perhaps find restoration from it out the other side, or when something new
happened, to restore them once more a measure of honor. In a way, our original sin problem is a manifestation of a shame problem that happened to us, causing us to be
born in shame by nature, in Adam.
Another thing the text note teaches is a
definite sign that a child was possible. It sets us up for the notice that comes later. The coverup will not stand.
There is nothing wrong, actually, with using the modern phrase "power dynamics" to describe particular aggravations (WLC 151) of sin. The redemptive historical reality of David's sin has such a monstrous quality, it is akin to Adam's fall. It makes Bathsheba's participation almost unnoticeable. She is simply overshadowed in the affair, and Scripture treats her with some measure of grace, kind of like it does Eve. She is not presented to us as a a woman of "brazen face," Prv.7:13.
The focus of the story is fixed on David, his adultery, his murderous coverup, his trampling of God's grace and his immense blessings. When we compare these sins of David to the sins that Saul committed, that resulted in the kingdom being torn from him and given to David, David's seem worse when looked at in a purely comparative light. If Saul was rejected for what he did in 1Sam, the book of 2Sam invites us to wonder how David could possibly escape an even greater rejection.
Bathsheba's participation, her compulsion, her trauma, her willingness, her victimhood, her shame, her profiting, her sorrow--so much of her story is simply lost behind David's massive culpability. I think, for spiritual readers and hearers of a more ancient time, they would have seen her situation as
shameful, per se. And for any or all the reasons we have come up with to place the blame on this and that, on one person or another. And in that, she is all of us, and we are all her.