Alistair Forbes was driving a Stagecoach bus in Broughty Ferry on 6 April last year at the time of the incident.
His vehicle hit pedestrian Keira Duff moments after she stepped off the kerb.
Forbes, who is no longer employed by the company, was also banned from driving for three months.
Dundee Sheriff Court was told that Ms Duff, 20, was injured in the crash but had made a full recovery.
Forbes, 58, of Dundee, was originally charged with dangerous driving causing serious injury.
His guilty plea to a lesser charge of careless driving was accepted by prosecutors.
Solicitor advocate Jim Laverty, defending, said: "He hasn't used a driving licence in a professional capacity since the incident.
"He is in the job market now and having his licence would be an advantage.
"He will not be applying for a driving job, however."
Sheriff Alastair Carmichael told Forbes: "You were driving a double-decker, a big, heavy vehicle, that needs to be driven with care.
"The careless element here is that you knowingly drove through a red light at a pedestrian crossing.
"The consequence was that a member of the public was injured, but thankfully has made a recovery."
A double-decker bus driver who went through a red light and collided with a pedestrian has been fined £400.