A report has identified extra costs including the removal of protesters from trees in Stapleton Road allotments and additional security measures.
Council leaders from Bristol, Bath, South Gloucestershire and North Somerset are expected to formally hear the news at a meeting on Friday.
MetroBus is part of a wider plan to improve public transport in the region.
"Unforeseen" design changes and ground conditions along with "hidden" gas pipes in Bradley Stoke have also contributed to the overspend.
Commuters have been enduring roadworks associated with the scheme in the city centre, on the M32 and various other locations in South Gloucestershire.
The "rapid transit" bus scheme was devised by the West of England Partnership, an alliance between the four councils in Bristol, Bath, South Gloucestershire and North Somerset.
It involves three routes: Ashton Vale to Temple Meads, Cribbs Causeway via Emersons Green to the city centre and the South Bristol link between the A370 Long Ashton bypass and Hengrove Park.
It will provide an express bus service on 31 miles (50km) of segregated bus-ways and bus lanes.
First Bus is expected to operate the scheme.
The cost of building Bristol's MetroBus project has risen from £203m a year ago to nearly £216m, the BBC has learned.