Hello and thank you for contacting Just Answer:
This sounds like a very frustrating situation for all involved. One approach that often works is called the "Ferber method". It is named for a doctor in Massachusetts named Richard Ferber. It explains how to help your child sleep in a series of steps designed to keep her there longer and longer. It does involve not responding to cries to get out of bed, which may be a bit troubling coming from a verbal three year old. However, I have many clients for whom this has worked and would recommend that you get the book from the library or book store.
I hope this helps and wish you luck.
I see. How about trying a behavioral chart in which she can put a star on each time she does not come in your room and after a certain amount of stars she can get a "prize". This would be a behavioral intervention using positive reinforcement.
If she forgets and comes in your room, perhaps you could gently remind her to get back so that she will get a star in the am. Often times, children help with the chart and decorate it how they like and she can pick whichever kind of stickers are her favorites and then know what she is working toward.
I hope that this approach will work for you.
Sorry that these suggestions were not helpful to you. You may want to consult with your pediatrician or have him/her refer you to a child therapist for some short term behavioral work.