At some point the men realised the victim had fallen off and, shortly thereafter, found him on the road having suffered a head injury.
They took Mr Grubb back to his flat, leaving him in the care of somebody else, before going to the party.
But at 3.15am that person became concerned about the man and phoned an ambulance.
Mr Grubb was taken to Dunstan Hospital and then flown to Dunedin Hospital where was placed on life support. After a few days, it was switched off and he died several days later.
Judge Michael Turner at sentencing said Mitchell exhibited a high degree of carelessness - the bike was faulty, no one was wearing a helmet and it was overloaded.
Despite the fact the victim's family asked for the man to be "given a chance", the judge said there was a need to denounce and deter the offending, both for the defendant personally and society in general.
Ms Guy Kidd said Judge Turner erred because he did not appreciate Mitchell would have employment while on home detention.
She said a community-based sentence would also allow him to better meet his responsibilities to his young daughter and pay child support.
But Justice Rachel Dunningham dismissed each appeal point.
"The Court of Appeal has acknowledged that in appeals revolving around whether home detention should have been imposed there is still a requirement to identify a 'material' error," she said.
"It can be very difficult in a marginal case to articulate reasons for preferring one approach to another."
Justice Dunningham said there was no evidence Judge Turner made a mistake in jailing Mitchell and, as a result, the sentence stood.
Mitchell had also been disqualified from driving for two years and ordered to pay $2000 reparation for emotional harm.