The word "Cyberbullying" is not an exact term. If they pass a law that just says "cyberbullying" is illegal without any specification then that should be held void for vagueness.
"Insulting" is not specific enough. People differ as to what they take as insults, and are not always reasonable about it.
And even if it is made specific that doesn't mean it will be constitutional. Speech is constitutionally protected. Driving is not. So the bar must be set higher for speech.
That being said the fact that something could be called cyberbullying does not mean that particular case is protected.
If it were possible to set up a third party that could decide what acceptable speech is and what isn't acceptable speech, that would obviate the need for free speech protections. The point of establishing free speech protections is that we do not recognize any authority as competent to decide what speech is allowed and what speech isn't. Outside of explicit threats of violence, and/or the digital equivalents of shouting fire in a crowded theater, "cyber-bullying" must be considered protected, because not all of us will agree that the targeted speech is cyber-bullying. If a majority opinion were enough to override the minority opinion in this matter, it would completely subvert the whole idea of free speech protections for individuals.
No, "Cyber Bullying" is not protected by Free Speech.
But, we must define what constitutes "Free Speech" and "Hate Speech" (which is the ABUSE of "Free Speech").
We have the Freedom of Speech, meaning we are free to speak what we feel. But, with that Freedom comes a responsibility, just as the freedom to drive a car entails we follow laws and regulations. Just as if you continually drove recklessly, day after day, being warned again and again, your Right, your Freedom, to drive would be revoked. The revoking of that persons Freedom to drive is not to protect him/her, but to protect the other citizens that could be killed by the reckless driving.
If someone abuses their Freedom of speech, using hate speech in blatant force to hurt someone, that Freedom can and should be taken away. Why? Because they abused that Freedom.
But most importantly:
There needs to be a definition though for both parties: The act of disagreement, non-support, or civil discourse does not count as abusing the Freedom, but using the Freedom responsibly. The act of berating, threatening, insulting, imposing terror, or any of the such does constitute as "Abuse" of the Freedom.
Freedom of speach is the freedom to speak your opinion. A personal attack on another human being is not an opinion, it is an assault of another person.
The simple fact words are being used to assault the person does not cover it under free speach. This is like saying the right to bear arms gives you the right to shoot other people.