I would be very careful about jumping in with bribes. I have raised 2 children, a son now a junior in college and a daughter who is a senior in high school. If you use bribery then it can become a power struggle if she decides the bribe is not enough and she wants more or realizes this is more important to you than to her then you are really over a barrel and I have watched parents go through this and it is not affective.
I would start by talking to her and trying to find out if something is goging on at school. This sets the expectation that grades are important and your expectations plus starts her thinking that these grades are important to her because they affect her life and opportunities, etc.... I would suggest emailing the teachers and seeing are her grades going down because she isn't turning in the homework, her test scores are pulling her down, her classroom behavior or participation is the problem, etc... That again gives you information to help direct her how to improve her scores and offer of help to her if "she" wants it. Let her know that you are "willing" to talk to her teachers if she need extra academic help and get tutoring if needed until she understands the material well enough to continue without help, etc... Again you are there to help and that you aren't going to let this just slide but in a positive proactive way. Sometimes this is enough to get the child more vested if nothing else just to keep you from intervining.
Remember friends are a huge influence, maybe it isn't cool to be smart around her so called friends or maybe she doesn't want to stand out at school for being smart, etc.... bribery will not solve those growing pains....Good Luck these middle school years are hard years but they do set the ground work for how she (and you) will approach challenges is high school and college.