1. Question Restatement:
In Numbers 5, what legal consequences might have been invoked - according to Biblical texts - if a woman refused to take the test of the bitter waters, like running away, refusing to drink, or even just verbally protesting?
Note: Omitting any analysis from the Talmud/Mishnah since it would be anachronistic to apply it to Ancient Israel, (since the Talmud was created 300 A.D., and the Oral Law was rejected and not observed by the Priests anyway.)
2. Answer, Exiled and Cursed:
The original form of this ritual test was to prove innocence, not guilt.
And by "original" - I mean, when the presence of "God" was to have been in the Temple / Tabernacle.
If the woman had fled, refused to drink, etc, the people would have assumed she committed "adultery" by default. Her own refusal would serve as evidence against her. And, she would likely/probably be stoned by a mob.
But, if everything was done legally, and "in order", there are Scriptural provisions that could have been invoked - so she would not have to take the test, or even die. ...
There are a few "catch all" laws in Scripture, that can essentially exile anyone from Israel for any breach, and
"refusal to submit to lawful authorities" would have certainly fallen into that category.
NASB, Leviticus 18:20 - You shall not have intercourse with your neighbor’s wife, to be defiled with her.
NASB, Leviticus 18:29 - For whoever does any of these abominations, those persons who do so shall be cut off from among their people.
NASB, Deuteronomy 28:15 - “But it shall come about, if you do not obey the Lord your God, to observe to do all His commandments and His statutes with which I charge you today, that all these curses will come upon you and overtake you:
At the very least, the woman would likely be "cut off" from Israel, (exiled, etc.), and if God wasn't merciful, then all the curses would apply too.
It is also possible that the husband might experience a "change of heart", and drop the accusation.
Frankly, this ritual could be seen as a mercy - as it probably would not have had the negative side effects stated in Scripture. (That is, God might have been trying to make sure that "mercy" would prevail). But, after the Priesthood and Legal System got corrupted - I think anyone in their right mind would have ran, (both women AND men).
An Objection Against the supposed "Advantage" of this Law, and against this as "a right women enjoyed", (stated in another answer and comments): Not only could men get rid of innocent women through a corrupt priest, but also: a woman could be used to provoke her husband, then be "proven innocent" by a corrupt priest, and then the man could be killed once a mob had been incited against him for "false accusation".
There is zero "advantage" in this system or "cause for enjoyment" - if God was not truly involved, (which the majority of Hebrew Scripture is spent on saying how he wasn't).