Police were called to the property in Ratho Station, west of Edinburgh, at around 9.30pm last Monday.
Officers believe it was not a random act, although no one was injured in the incident which saw a nearby stretch of the busy A8 road shut for around 14 hours.
Police Scotland say they will be stopping vehicles tonight in Glasgow Road that may have been in the area at the time.
Officers particularly want to trace a motorcycle believed to have been on both carriageways of the road before the shots were fired, and which travelled along the road afterwards.
The bike made its way onto the city bypass, via Gogar roundabout, police said.
Detective Chief Inspector Stuart Houston, leading the investigation, said: "The investigation has established that following the sound of shots, a dark-coloured motorcycle made its way at speed along the A8 dual carriageway past the entrance to the Royal Bank of Scotland, and thereafter towards the Gogar roundabout before makings its way onto the city bypass.
"I am keen to trace the occupants of a dark-coloured, seven-seater vehicle which was also travelling on the roundabout at this time and may have had to take evasive action to avoid a collision with this motorcycle as it entered the roundabout."
Anyone with information can call Police Scotland on 101 or Crimestoppers anonymously on 0800 555 111.