The initial death toll of 13 rose to 16 and then again overnight as people who were transported to hospitals succumbed to their injuries.
It wasn't immediately clear what caused the driver to lose control of the bus, sending it 40 meters down into the ravine about 18 miles from the capital of Podgorica, police said.
Romanian officials confirmed Monday they had sent a plane to Montenegro from Bucharest to transport the 27 surviving passengers.
A 12-year-old boy who was on the bridge at the time of the crash was also injured and taken for treatment.
"The driver drove a little too fast and the bus slid," said Carmen Dorobet, a survivor of the crash.
The highway through the mountains of northern Montenegro towards the capital is a site of frequent crashes, where winding roads and slippery surfaces cause dangerous driving conditions.