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You're correct that college is a great opportunity with a scholarship and not worth losing this.
You are finding yourself in a catch 22 as to how to persuade her to stay in school and seeing how the relationship with her boyfriend is the possible cause for her wanting to come back home. You could point out to her that at a young age relationships often change but being fortunate to get a scholarship and and acceptance at college is not something every one gets. It would be difficult to persuade her to do what is best because at this age she thinks she knows what is best for her and may try to prove her point.
It may be a good idea to see if she would be willing to listen to another close family member or see if a counselor can assist with this in a family session.
The job market is not doing well and you could let her know that it is hard for folks with education and years of experience to find work and how much harder it will be without education. Prompt her to engage in self examination and some soul searching and ask her where she sees herself in 4 years with a college degree and few years older or without. Journaling and writing down the pros and cons may help.
Family therapy is what would need to be considered at this time as you have exhausted your options as you said. Bribes won't help her; it will only teach her that people get what they want irregardless of consequences and that on top of it get rewarded.
If she is to reside in your home and not go to school then you may want to tell her to get a job and start making contributions to the family. That is usually what adults do and if she is choosing such life without education she ought to see how money is earned and what life is out there with the little money earned and not many opportunities without education.
You may want to find out if it is just the boyfriend issue that brought her home or if she is having some confusion as to what subject to major in college. That at times can be anxiety provoking to the student as they do not want to disappoint others and fail themselves as a student. Hence give up all together.