I don't like watching bullying happen around me, but how do I stop it without being bullied myself?

Tell a teacher, or get your friends to help you stand up to the Bully/s so you're not on your own, or maybe invite the person who's getting bullied into your friend group or just to be your friend, so that they're not alone all the time.

When I come across this situation I will usually approach the person being bullied, address them in a friendly manner, tell them I am meeting my sonS, invite them for coffee and then ask if the other people/person is their friend. Usually it works but if I sense it won't then I call the police or call my sons depending on the situation that would help the person more quickly. If they are young I just intervene to get the one being bullied out of harms way and find out where the bullies live and go speak to the parents.

If the bullying happens in a school or at work, go and talk with a teacher or the boss at that work place. Tell them you want to be anonymous. And tell them in a way that they will take it seriously and do something about it.

Ask adults (like teachers) to help you. Ask others to help you. (This never worked for me though but you might have better luck. I got bullied regardless of what I did) Bullies tend to target vulnerable kids so, find a whole bunch of friends to be friends with the person that's being bullied. Give them a group to join. (I was alone when I was in school) But honestly you can't change bullies. You can stop one kid from being bullied and that bully will find somebody else, cause that's what they do. That's why they're called bullies. But if the question is about not wanting to watch bullying happen around you, why don't you just move schools or workplaces? Or stay at home, be homeschooled? Maybe you'll be able to find somewhere where bullying doesn't happen, so you don't have to watch it happen.

Identify your weaknesses and slowly build on gaining self-confidence and self-esteem, that will make you far less vulnerable to being bullied

Unfortunately you take a risk being bullied yourself when you stand up for someone else being bullied. If you do it you just have to let the insults be "water off a ducks back". It takes a lot of inner strength

In situations like this I find going to someone in charge, whether it's a professor, teacher, boss, manager, guidance counselor, or someone you confide in they tend to have the ability to help and give the bullied resources for them as well. Teachers are now required to report signs of abuse and bullying, and are mandated reporters themselves. It's scary, but in my experience, it is the easiest way to stop the bullying in its tracks. Talking to a professional afterwards, a therapist for example, I also found helpful because it helped me figure out that I didn't deserve the treatment the bullies were giving.