The judge added: "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, now of Ramsgate, Kent, was suffering from "emotionally unstable personality disorder". At an earlier hearing, the court also heard how Cowan was addicted to laxatives.
She sobbed throughout the hour-long hearing. Prosecuting, Peter Forbes revealed how Cowan had created an alter-ego in the name of Farina La Rose, with her own date of birth and claiming to be a child murderer.
Cowan also created accounts in the names of "Bulger's Ghost" and "John Venables" - one of Jamie's killers.
He said: "She created another called Life Of LaRose receiving texts in which she said she got goosebumps from lifeless infants and on that internet site were pictures of children on train tracks."
Cowan was arrested after police launched an investigation when Mrs Fergus complained about trolls on Twitter blaming her for the death of Jamie in 1993.
Mrs Fergus tweeted: "Cant believe that some1 on here is still blamin me 4 my sons murder it took me a long time 2 stop blamin myself thanx 4 ruinin my evenin (sic)."
After a picture of a relative of Mrs Fergus was posted online, Cowan, using the username SirJVenables, taunted: "Can't wait til he's a tot, the tracks are already calling his name" - referring to the brutal murder of Bulger.
Other messages sent between February and May 2014 were "particularly cruel," the prosecutor added.
One of them - in which Mrs Fergus was tagged - 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."
A victim impact statement made by the mother - who had been expected to attend the hearing - was given to the judge.
Judge Williams added: "In it she explains she has at times felt unable to leave her house and has locked herself away in her own bedroom."
Mrs Fergus told police she thought the messages were disgusting and added: "You can't keep targeting me like this... this just brings it all back and is mocking Jamie's death. This is mental cruelty and you shouldn't be able to write this and get away with it. It is just pure cruel."
Andrew Espley, defending, said that as a result of what Cowan did she had received numerous death threats.
Cowan was also given a ten-year ban from contacting Mrs Fergus or her family.
