Bird, a 52-year-old father-of-two, killed 12 people and injured 11 more in various locations around Cumbria before turning the gun on himself.
Speculation has centred around two disputes he is reported to have been involved in prior to the rampage.
One stemmed from a long-running argument with cab drivers over passengers. A taxi firm owner who used to work with Bird has spoken of the killer's grievance with people he believed had taken custom from him.
Mr Goulding said that police were looking at why certain individuals had been singled out by the gunman.
He said: "A key part of the 'why' in this inquiry is to try and establish why those killed were chosen. Because of a motive, because of a grudge or simply random killings. Our initial assessment shows we have a combination of both and I will not speculate further at this time
