2 Samuel 11:5-6 The woman conceived and sent word to David, saying, "I am pregnant." So David sent this word to Joab: "Send me Uriah the Hittite." And Joab sent him to David.
Bathsheba goes to David to "fix" the problem. There weren't a lot of choices in this day and age. The law stated that adulterers were murdered. I'm sure Bathsheba considered the odds of taking the full brunt of this sin - because David was King - would they really kill the King for this?
Bathsheba was taking a risk - when David heard the news, he calls for Uriah - Bathsheba's husband to come home. At this point, no one knows what David's plan is - least of all Bathsheba.
He could've called Uriah home to tell him that his wife had been unfaithful and that she needed to be killed. He could have had her killed. This must have been a true time of stress for Bathsheba.
Many times, our stressful situations are ones of our own making. That doesn't make them any less stressful. The only way to work this out is to take it to God and confess. The consequences at that point - will be God's choice. If we have a repentant heart, God loves us and even He can take our sin and use it for His glory. Don't ever think that your sin is so bad that God can't use you. Even in the darkest hour - if you cry out to God - He can and will be there with you - even through the consequences.