Police say a 61-year-old man boarded the bus near the roundabout at Kenrick Way and Kelvin Way, on Thursday afternoon and started threatening the driver with a bottle.
Two men tried to intervene but one ended up being stabbed in the neck and the other suffered an arm injury.
A man was arrested on suspicion of wounding and remains in custody for questioning.
Police are encouraging witnesses to come forward.
A West Midlands Police spokesperson, said: “We’ve arrested a man on suspicion of wounding after two men were stabbed with a broken glass bottle on a bus in West Bromwich on Thursday.
“It’s understood the 61-year-old got on the bus near the roundabout with Kendrick Way and Kelvin Way at around 2.25pm and began abusing and threatening the driver with a bottle.
“Two men on board the bus tried to intervene; one was stabbed in the neck and the other suffered an arm injury.
“The suspect remains in custody for questioning.
“We’re appealing for any witnesses, particularly anyone who was on the bus at the time, to get in touch and quote crime reference number 20/377389/22.”