Eight people were hurt in the terrifying incident, which happened around 11:10 p.m. Thursday.
Authorities say the 55-year-old driver was attempting to turn left off University Avenue onto a ramp to the Washington Bridge when the Bx35 bus suddenly veered off the road.
The MTA said the GPS revealed the bus appeared to be traveling at 17-26 mph during the incident.
Transit officials held a briefing Friday to discuss the incident.
"We know the speed limit on the road is 25 mph, but the appropriate speed for taking a turn such as this is between 3 and 4 miles per hour," MTA Chief Safety Officer Pat Warren said. "So we can say at this time while the investigation is ongoing, speed is clearly a factor and is obviously of great concern to us."