The bus was left with a smashed front windscreen after the crash on Corstorphine Road at 5.20pm yesterday.
Police said the only injuries suffered were by the drivers, who are not thought to be seriously hurt.
Police reduced a section of the road close to the Murrayfield Hospital to one lane last night while a recovery vehicle towed away the bus.
Elsewhere, firefighters were called to tackle a blaze at a row of disused cottages in south Edinburgh.
Crews were called to the buildings opposite the Straiton Retail Park at around 8.40pm.