Sorry for the late reply, I missed your comment originally. I haven't been able to replicate this issue, so I can't guarantee this will work, but it did get rid of the dryad when it was chasing me normally, so it should work in your situation as well. https://mega.nz/file/UOwR0RxS#2m4gbab4MACoOcC-ob6ne-0sOg-8pbM4x1HD-RQ_5To
If you apply this patch there will be a new option in the debug item menu called "persistent dryad", using this should get rid of that dryad.
If it doesn't work, then I've got a few more questions to try and figure the issue out. (If it did work, you don't really have to answer this.) First off, does the Dryad immediately start chasing you when you enter the Depths? Or only when you go south? Does she still jump out of a bush after it rustles, or does she immediately sprint after you once you get close enough? If the bushes still rustle, you might be able to avoid her by hugging the left or right edge as you progress. Let me know if the bug is persisting.