Often a place where bullies exist and thrive says a lot about what is considered "normal" in there. This means, the system and culture instead of inhibiting such behaviours is shying away from intervening and stopping this behaviour. If there is an indication of a bullying behaviour, the right thing to do is to bring this behaviour to attention to the bully ideally directly. It may be the case that the bully is unaware that they are behaving in such a way and perhaps did not receive feedback in past about the same.
If the bully is defensive or could get aggressive on receiving feedback, I suggest to prepare for such feedback especially on how to approach that situation. Preparation is really useful in such cases, and helps you to deal with their stance in a constructive way.
An indication of a bullying behaviour requires a leader to act immediately and if this behaviour is demonstrated in a group setting, it is better to resolve the group and reach out to the affected person as soon as possible. If you as a leader can treat the situation of bullying as an urgent and important matter, it sets the tone in the team and to the bully that such behaviours are not accepted. I also suggest from my past experience that you reach out to the others in the group to be mindful of such behaviours and bring it to your attention as soon it occurs. In my experience, I had this situation with some one who would be a bully in a public space on slack. The first time this happened, I reached out to them in private and shared my observation and asked for they think of it. They were unaware that they were the bully in how they communicated on Slack. I also reached out to the affected person to make sure they have a chance to express their emotion and I reassured that such a behaviour is not tolerated. I worked with my leaders to formulate a communication guideline for everyone on how to recognize and address such a behaviour after consultation with the People / HR Team. The bully here was also asked by me to take up mentoring from peers who were better emotionally aware and guided them to change their communication style.
However, in some cases, this is hard to change and then I suggest to have the hard talk with the bully and involve the People / HR Team in this. It is better to give the bully an indication that if this behaviour repeats, it will lead to termination.
This is one of the many things that were discussed in the last Leadership Bootcamp cohort. If you are interested in future cohorts, signs up are open now.