There is no harm in applying, but I don't think you have a realistic chance at being hired.
The email she wrote basically complies with the bare minimum legal requirements of how jobs are posted and the process of hiring. She can't tell you NOT to apply or that you WON'T be considered.
She may not remember all the details, but she will - and likely does - vaguely remember "bad experience, did not work out." Sometimes that can be worse.
Whether or not you have matured or become more qualified in the intervening years won't "fix" the bad impression you left, nor will an apology or explanation. In the same shoes as this professor, I would not recommend hiring you on the hope that you've matured, unless there are no other qualified applicants AND someone must be hired.
I hate to be harsh, but I imagine I am less harsh and demanding that this former supervisor. So - yes, by all means apply, and if by some chance you do get invited in for an interview, just do your best to express why you are the most qualified person NOW for the job. However, I wouldn't expect to get the position.