The sin of David, rape?

Bathsheba was hidden from the view of men. Only from the parapets of the palace could she be seen (perhaps even unknowing to herself - a lot of women KNOW when they are enticing men and like the attention; many do NOT know).

I see no sin on the part of Bathsheba, while all of the bloodguiltiness is upon David. HE looked down on this sacred ritual mikvah (ceremonial bath after menstruation) and could have simply looked away. HE called her and when the king calls, everybody listens (life and death). HE had sexual relationship with her. HE tried to arrange for the coverup. HE had her husband killed. HE added her to his harem.

David is the problem here.