What happened to Bathsheba?

I can't understand why David in Psalm 51 says "Against you, you only, have I sinned". It seems to me the person he let down most was Bathsheba. But why doesn't she get a mention in his apparent guilt as expressed in this plea for mercy?

As I think about how ineffective I am as a Christian I often think about how I let people down. I can't get into this "I'm off to heaven so I'm alright" bit and I often feel like I would feel more at home with the let down people, who according to some people's interpretation, are destined for the more warmer climate of 'down there'. If we sin against another person, whatever that sin is, we destroy another chance for them to have confidence in the gospel. Is that right?

Then in Matthew 18 v15-17 Jesus tells those who have been sinned against to go and tell the culprit. What did Bathsheba do? Did she say to David "With God on your side I assume you will get away with this?"

God's grace was once again exploited.