Not legal advice
I want to applaud the mhchameleon423 (OP) for seeking whatever options necessary to provide the child with the appropriate care and help she needs...to protect herself and others. I also want to acknowledge the contributors to this thread who have refrained from judgment. Your empathy speaks volumes to your commitment to the purpose of this site.
I am fortunate to be the parent of a mentally healthy child, I grew up in a family with a mentally ill sibling. The toll was, and remains, quite high. I do have a child who has a chronic illness that has presented a tremendous financial burden even with 'good' insurance. With each test, lab visit, and hospitalization...how I would afford it was a huge concern...with a situation like this with no end in sight, for these parents to seek whatever alternative available to get the help their child needs without losing everything is fair...they do need to survive, provide for other children and so on. A TPR is huge, but if it's what it takes...it's what it takes. But as has been advised, it's not a slam dunk.
It is clear, mhchameleon423, you have considered the collateral damage of this action, not just for your child, but yourselves, as well. But in your view, that damage is far less than the loss of your child's life or harm to others. There is far too little support or 'education' for parents of mentally ill children...
If your child has clinical diagnoses of the conditions you state, have you applied for disability support for her? If not, you NEED to. This may also provide you with additional support. This is not going to end when your child turns 18...it will last her, and your lifetime. Getting as much support and benefits as possible as early as possible will benefit all in the long-term.
Has your daughter's mental health provider recommended or ordered residential treatment? If it has just been recommended and not ordered, insist it be ordered and deal with the financial issues later...they can ALWAYS be negotiated after the fact. If your daughter is the risk to herself or others you claim in your post...this is necessary. Fight for it.
Have been advised that your child should not be left alone or with other children unsupervised? Is the school aware of her diagnoses and this recommendation? If so why is she still in school (as your posts suggest) and why is she still riding the bus. The teachers and bus drivers cannot supervise 100% of the time (far less than you can). I am not an attorney, but if something did happen, with this knowledge, IF your daughter hurt another child , you could/the school be held legally liable?
This is a hard, hard situation...but with the right guidance, help and support you and, with all hope, your child will survive it. Life may not be what you hoped for any of you...but it can be better.
I wish you all the best possible outcome.