Chair of the bench, Catherine Hobey-Hamsher, said: "A reasonable person would have stopped immediately.
"It is a silent danger, coming up behind people - they have no idea.
"And, above all, it diminishes the really rather low esteem cyclists already have.
"People do not like cyclists, and you are doing nothing to enhance their reputation."
De Carne said the incident happened because he "panicked" and that he cycled home to relieve pressure from his fast-paced city job.
PC Neil Hossack told the court De Carne cycled dangerously, changing direction and cutting across the path of a marked police car, which had to brake.
The banker then continued to cycle despite being followed by the police car, which had its blue lights and even rode down a busy side street packed full of people.
PC Hossack said: "A police car followed you, in order to speak to you about your cycling. As it pulled behind you, you did not stop."
Asked if he had anything to say, De Carne said: ""I admit the offences. I panicked, I thought I could continue cycling and I lost control.
"I am ashamed of what I have done, and it's a humbling experience, and again I am sorry.
"I am fortunate obviously that nothing serious happened at that time of evening, and it's been a stressful experience.
"I stopped as I realised the gravity and the reckless behaviour I was performing, and I spoke with the officers.
"I have tried to learn a lesson of what I was doing."
He added: "I cycle because it takes pressure off when I leave work, but I am now trying to change and enjoy the experience."
The banker said he had taken part in a cycling safety course, and had tried to change his behaviour.
De Carne was also made to pay £85 in court costs and a £125 victim surcharge.