It is the second time such a collision has happened since the controversial Edinburgh trams system first started running at the end of May although no-one was injured in either incident.
The entire tram service was closed down for four hours and the incident, which happened at West Maitland Street at around 7.45am, caused severe congestion at one of the busiest times of day.
The tram operators said its driver was not at fault, while the bus company said its investigation into the accident was ongoing.
Edinburgh's Tory Group leader Cameron Rose said the traffic priorities at the West End should be reviewed. He said: "It raises concern about traffic management in the event of a fault or collision.
"The time has come to review this (traffic arrangement) in light of this."
First Minister Alex Salmond is setting up a public inquiry into the trams.
Police Scotland said both bus and tram were travelling towards the city centre when the collision happened and traffic diversions were put in place. Dalry Road and Haymarket Terrace were affected and the road was blocked southbound at Palmerston Place at West Maitland Street.
It is the latest crisis to hit the trams in the three months since the troubled £776 million system started running late and over-budget.
The system was closed down after balloons caught in an overhead line and the entire service halted after a tram broke down at Haymarket.
The July collision, which also involved a bus, happened at Manor Place, near the Shandwick Place stop in the West End.
A teenager was also hit by a tram in June but was uninjured.
Edinburgh Trams said a FirstGroup bus hit the tram in West Maitland Street at around 7.45am yesterday.
A spokesman for Edinburgh Trams said: "After recovery of the bus by a tow truck, engineers were able to assess the tram on street and drive it back to the depot where a full damage assessment will be being carried out.
"We've reviewed our CCTV footage and are satisfied that our driver was not at fault and that our procedures for handling an incident like this were followed appropriately.
"We'd like to apologise to any passengers affected by the incident this morning."
A spokesman for First Group said: "We can confirm that one of our service 38 buses from Falkirk to Edinburgh was involved in a low speed minor incident in Edinburgh's West End.
"We have launched our own investigation to establish exactly what happened."