Going back to university after suspension, how do I move past the shame?
The university suspended you, which is a signal that it is still willing to have you as a student after serving your suspension.  (If it wasn't, you'd have been expelled.)  Therefore, upon your return, this professor (and every other professor) has the same professional obligations towards you that she would to any other student: to accept you in her classes, to treat you with courtesy and respect, to help you learn the material, to grade you fairly based on your work and the standards of the course.  It is possible that your assignments may face extra scrutiny for plagiarism, but hopefully that is irrelevant as you're not going to do it again.

It's possible that relations may be strained between you, but I think this may be more on your side than hers.  Speaking for myself, I certainly find it disappointing when a student cheats, but it's not as if I'm going to declare a personal vendetta against them and seethe with fury every time I pass them in the hall.  That would be unprofessional, and not worth the emotional energy anyway.  We go through the disciplinary process, I hope that they learn their lesson, and it's back to business as usual.  If they are able to turn things around and show genuine interest in and dedication to their studies, for me that's ultimately uplifting.

So if you want to take her class at a later date, by all means do so.  You might find it helpful to talk with her first: express your regret over the incident, as well as your continued interest in your subject and in completing your degree.  I think it's very likely this will help clear the air for both of you.  It would be wise for you to be extra diligent about quotations, citing sources, etc, and to consult your professor if you have the slightest question about any such issues.

Maybe she won't invite you to dinner, and she probably won't be the best person to write you a letter of recommendation.  (Even if you get to be on better terms, which I hope you will, she might still feel it's her duty to mention the cheating incident in any letter she writes, which is probably not good for you.)  But I don't see any reason you can't have the same basic educational experience as any other student.