Cowan, a 20-year-old student created fake social media accounts in the names of Farina La Rose, claiming to be a child murderer. But also, 'Bulger's Ghost' and 'John Venables'- one of Jamie's killers.
One message sent between February and May read: 'The anniversary of my death is like a giant pigeon forever crapping on your heart.'
Another said: 'You all know who I am, the lad who abused Jamie Bulger, hahaha.'
Judge Adele Williams said: 'Your offence involved sending the most vile and degrading messages via Twitter to Denise Fergus.
'In my judgement you have shown no true remorse and no insight into your offending.
'This is maybe because you cannot show true remorse or insight.'
A psychiatric report revealed that Cowan was suffering from 'emotionally unstable personality disorder'.