You can see some students on camera and hear others off camera taunting the woman about her weight.
The students also talk about threatening to go over to the bus monitor's house and steal from her.
Greece Central School District has asked YouTube to take down the video.
Spokeswoman Laurel Heiden said their bullying response and prevention team was activated and all students involved will face disciplinary action.
Greece Police are questioning four middle school students and will decide if charges will be filed in juvenile court.
It's unclear when this incident happened.
The Greece School District said the bus monitor is Karen Klein, who has worked there for 20 years and became a bus monitor about three years ago.
13WHAM's Patrice Walsh spoke with Klein Wednesday afternoon. She said the comment that hurt the most was when the kids said "you're so ugly your kid should kill themselves." Her son took his life 10 years ago.
Greece Bus Monitor: Students Should Be Punished
Greece. N.Y. - Karen Klein says she heard students on the school bus call her fat but she tried to ignore it.
She didn't realize how bad the taunting was until she watched the YouTube video that has sparked outrage.
Cell phone video shot on a school bus Monday shows a small group of Greece Athena middle school students bullying Klein about her weight and threatening to come over to her home and steal from her.
Klein, 68, spoke to 13WHAM's Patrice Walsh at home about how much the comments have hurt her.
"I tried to ignore it...I didn't hear some stuff and tried to shut them out," Klein said.
She was horrified and hurt and she wishes she would have done more to stop the students, but felt helpless.
Klein did tell the bus driver and co-workers about the incident but she didn't think much would come of it.
One comment from a boy on the bus was especially hurtful because he said Klein "didn't have a family because they all killed themselves because they didn't want to be near you."
Klein's oldest son took his own life ten years ago.