I really don't want to do it.
Go with your gut. Not wanting to join her on this trip is enough.
How on earth can I approach her with this? I feel terrible for having been dishonest
1. You could tell her everything and say no. She will likely feel overwhelmed and blind-sided and will have a lot of questions.
2. You could simplify and come up with a one liner, something like, "This isn't a good time for me to step away. I hope you have a great time, though."
3. You could provide a scheduling conflict as a reason you can't go, or perhaps even suggest an alternative plan with her that would require less time together.
None of these are ideal, and maybe you'll come up with another option. Just trying to get the creative juices flowing. Think about what will work best in your scenario. For now, I might suggest buying yourself a little time and think about whether and when to tell her your reasons.