Bathsheba is best known because she was the object of David's adulterous affection. The way the story is usually told, a powerful and impulsive king, overcome with desire, swept an innocent young woman away into his chambers and then had her husband killed to cover up their crime. As with most things, there is more to the story.
To piece the story together, it is important to know just who Bathsheba was. From the story in 2 Sam 11, we know she was the wife of Uriah the Hittite. Of equal importance, she was the daughter of Eliam (2 Sam 11:3) and the granddaughter of Ahithophel (2 Sam 23:34).
A close reading of 2 Sam 23 reveals that both Uriah and Eliam were members of David's mighty men. It appears that they had been with David beginning with his time in the wilderness and formed the core of his forces during his rise to the throne. Placed in this context, David's behavior was especially vile. He betrayed and killed a man who had been close to him and loyal for many years.
Bathsheba's grandfather was Ahithophel who was David's counselor (1 Chr 27:34) Ahithophel never forgave David for his behavior with his granddaughter and her husband. When Absalom siezed power and drove his father out of Jerusalem, Ahithophel stayed behind and became chief advisor to the rebellion (2 Sam 15:30-31). It was he who advised Absalom to sleep with David's concubines (2 Sam 16:20-23).
Her pedigree casts Bathsheba's bathing on her roof into a different light. It is certain that she and David had known each other for years and that Bathsheba had grown up in the royal court. In other words, the bathing incident smells as much of enticement as it does of chance.
Two other incidents will round out our understanding of the lady who was Solomon's mother. Both were during the struggle for who would succeed David upon his death.
Adonijah the son of Haggith took steps to have himself declared king as David's health failed. He assembled a following which included significant members of the army and the priesthood (1 Kings 1). It is in this context that we find Bathsheba conspiring with Nathan to have David anoint her son Solomon.
When the ploy succeeds in elevating Solomon to the throne, we come to the second incident. David had had a concubine at the end of his life named Abishag. When Adonijah spoke of the concubine to Bathsheba, Bathsheba told Solomon about the conversation. Solomon's reaction was immediate and violent. He had Adonijah killed. In that culture, for a member of the royal family to take the concubine of the former king was to assert his title to the throne.
In both of these incidents, the Bible records Bathsheba as being the responder - first to Nathan and then to Adonijah. While I'm sure that the conversations are accurate, it is curious that three times she is in just the right place at just the right time to move the story forward and establish her place in the royal line.
The Bible is sparse in the detail of its stories. If it were written as a novel, it would require many more volumes to hold all of the stories. It does, however, provide sufficient cross links to enable us to discern the motives of many of the actors. That is certainly the case with Bathsheba.