There are no security guards on Greyhound buses. The only law and order while you are traveling on the bus is the bus driver. He/she is the go to person if you have an issue and they have pretty much unchallenged authority when it comes to kicking someone off the bus.
There are security guards at some of the Greyhound bus stations, however. They are usually at the larger stations or the stations that are known to have security issues. Chances are if you see a security guard at a Greyhound bus station then it’s a place where you need to watch your back. Greyhound is far to cheap a company to spring for security unless it’s absolutely necessary.
The security guards will not bother you for the most part if you have a ticket and are a Greyhound customer. In some very rare cases security will do bag searches but these usually happen in conjunction with law enforcement or at stations near the border where drug trafficking is high.
If you run into an issue at a Greyhound bus station don’t hesitate to alert security. If you are at a station where there are no security guards talk to your driver or another Greyhound employee. They will have no problems calling the cops and the cops are used to coming to Greyhound stations so they should arrive fairly shortly thereafter.
Bottom line: there is pretty much always someone you can turn to for help while you are traveling via Greyhound even if they aren’t a security guard.