Sentencing the trio at Manchester Magistrates' Court, chair of the bench Joe Bangudu said: "This was a short-lived but disgraceful incident."
All three pleaded guilty to a public order offence of using threatening abusive words and behaviour, or disorderly behaviour, likely to cause harassment, alarm or distress, and the judge added: "Your language, although described by your defence as industrial, we think was vile and therefore unacceptable directed to anybody.
"The location where you chose to display your drunken behaviour was in a public vicinity, with not just Mr Jones in that proximity.
"There could have been kids that could have been affected by your behaviour. No-one should ever have to put up with such language and behaviour.
"We have not seen any sort of remorse by you. That is a concern."
Carl Miles, prosecuting, said Jones was travelling on the train the following day after his team's loss in the Six Nations fixture.
On the journey were a number of rugby fans including the defendants who had not been to the game at Murrayfield.
The defendants also alighted in Manchester and initially spotted Mr Jones' driver on the approach outside the station as one of them commented to him he was "smartly dressed".
They then turned their attention to the arriving Jones and asked him for a photograph.
The court was told Mr Miles said: "Mr Jones consented and, realising they were opposing fans, he may have done so to diffuse the situation. Then things began to become a bit more disorderly."
As the driver ushered Jones into the vehicle, one of the group rubbed the coach on the head and attempted to kiss him on the head before someone said: "You f***ing baldy c***".
Swearing and chanting continued and the phrase "you f***ng baldy c***" was repeated as the car door was opened by Grant.
The driver described Jones as appearing to be "quite shaken" and believed the incident could have escalated and "may have become physical".
The court was told that Jones did not wish to make a statement on the incident.
Footage of the incident circulated on social media at the time and the defendants voluntary attended police stations following a media appeal for information.
Matthew Wallace, representing all three defendants, said: "I think it is fair to say he (Mr Jones) is somewhat of a divisive character.
"It is clear that this is somebody who has gone out of his way to upset fans from various rugby nations in recent months."
He cited Jones's comments about the "scummy Irish", Wales being a "s*** little place" and the questioning of whether Scotland could "handle expectations" ahead of the England game.
The defendants only wanted a photograph, he said, before an amount of banter followed in which "industrial language" was used but that Jones had also been abusive to one of them.
Mr Wallace conceded "things got out of hand" and "they went too far" as Jones walked away from them but he added: "It was not conduct that is threatening. No-one is trying to hit him or manhandle him. We are talking about the space of 10 seconds. That is the length of the incident.
"They had had a drink. They met a divisive character who you would expect engages in banter in different directions. That person does not make a complaint."
Responding, Mr Miles told the court: "Ribbing and banter that occurs during the course of game is in a sporting environment. Mr Jones is on his own time here. You don't expect to see a group of individuals swearing at people while intoxicated."
Shouts of "Freedom" were heard as the defendants later left the court building.
A fourth defendant, Dale Cleeton, 25, also of Carrick Knowe Avenue, pleaded not guilty to the same offence and will go on trial on August 10.
Cleeton, of Carrick Knowe Avenue, was fined £120, Inglis, of Cornhill Terrace, received a fine of £105 and Grant, of Drum Crescent, was given a financial penalty of £140.
All three were also ordered to pay court costs of £115 each.
Mr Bangudu said Grant had prolonged the behaviour and language by opening the car door once Mr Jones was inside.
Mr Jones said in the wake of the abuse he will never travel on public transport again as it was believed he feared for his safety.
After England's 25-13 defeat by Scotland, the Australian initially posed for selfies on the 9.15am train to Manchester from Edinburgh Waverley before the fans ripped into the coach for his team's dismal performance.
Scottish Rugby described the abuse suffered by Mr Jones as "disgusting behaviour" and in a statement, the SRU said it was "appalled".
"The disgusting behaviour of those involved does not represent the values of our sport or its fans," the statement said.
"The dignity Eddie and the England team showed on Saturday is in stark contrast to this ugly incident."
Video footage obtained by the BBC's Dan Roan shows Jones posing for selfies, before being verbally abused.
The England head coach disclosed in the days following the incident that it was an "uncomfortable" experience, one that "massively surprised" him and one that he would not be repeating.
Mr Jones said: "I try and do the right thing by the fans but if that happens then you've got to have a look at your own safety. I never knock back a request for a selfie unless I'm racing to somewhere. I did a lot.
"For me to travel on public transport, I thought was OK. I'm a human being. I don't consider myself any different from anyone else. But I'll make sure I won't in future. It's as simple as that. I can't. Because it was shown on Sunday what happens when I do.
"That's the world we live in. It wasn't comfortable. It was a bit of both [physical as well as verbal]. After a loss, no I wouldn't [do it again].It's [all] part of the challenge.
"When I came to England, I knew there were going to be challenges. As an Australian coaching England, there were always going to be challenges and that's just one of them."
While he did arrive safely and was able to take his seat alongside Sir Alex Ferguson for the game between Manchester United and Chelsea, there is little doubt Jones was shaken.
He declined to go into detail, stating that he "did not want to make a big deal of it". But he did make one telling point as to the invective that swirls around such fixtures.
Jones said: "If you're in a position of responsibility, you've got to be careful what you say. Because if you talk about hate and you talk about rubbing peoples' noses in the dirt, and all those sorts of things, it incites certain behaviours. Are they the sorts of behaviours that we want to see?"
Scotland prop Simon Berghan, despite being born in New Zealand, had to return to a press conference before the game and correct himself after he had spoken about the traditional "hate" for England.
Former Scotland captain Gavin Hastings was quoted in the build-up to the Calcutta Cup clash last week as saying that although he admired Jones, "as a supporter of one of his opponents, you just want to rub his face in the dirt".
Jones also disclosed that he had once had a similar experience when attending a match at Bath. He had not thought to request a Rugby Football Union escort or car to be laid on as he considered himself to be on a private visit.
As journalists pressed him to elaborate on the incident, Mr Jones admitted he was surprised: "Massively, but that's the world we live in. I don't want to get into it, guys. I don't want to make a big deal about it. It's over and done with."
