The horrifying incident occurred in southern Russia, near Crimea, earlier this morning.
Officials said 20 people had been saved but some men were still missing.
Eight people have been injured, with five in a serious condition.
They said rescuers equipped with scuba equipment are searching the water for any survivors.
There were unconfirmed claims that between 38 and 60 people were in the bus when it sank at a depth of around 35 feet
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An eye witness said: “The bus fell from the end of the pier. It was a big vehicle with dozens inside.
“Some minutes after the fall some people managed to swim out but others probably fainted and could not swim.
“The divers reacted quickly.”
One local said: “About 10 jumped out when it was falling, but others ended in the water.
“The depth of the sea is about 10 meters there.”
The Russian Investigative Committee, the equivalent of the FBI, has launched a criminal case into a suspected traffic violation that led to the deadly incident in Volna on the coast of Kerch Strait.
It is unknown how the bus, which was ferrying construction workers to a pier, ended up in the sea.
Russian news agency TASS said: “The bus belongs to the company that is building a pier for the Tamanneftgas oil and gas company, the Emergencies Ministry said. It was carrying shift workers.”
The bus has now been removed from the water using a crane.
More to follow…
Additional reporting by Will Stewart.