The blue Yamaha was found on the carriageway about 1.20pm, and two men were seen walking away from it, and getting into a white van that was nearby.
Police are now appealing for anyone who may have seen what had actually happened with the bike to contact them.
A police spokesman said:
We are working to establish exactly how the bike came to be abandoned on the road on Sunday afternoon, and would appeal for anyone with any information regarding this to get in touch.
The people involved in the accident have never reported it, and we are keen to identify the rider to ensure they were not injured as a result.
Anyone with any information should contact Lothian and Borders Police via: