Figures obtained by The Herald under Freedom of Information laws reveal 193 fixed-penalty notices were issued to cyclists by Lothian and Borders police in 2012/13, just before the creation of the single force. This compares to just 99 two years earlier and 119 in 2011/12.
The £30 fines can be issued for offences including cutting through red lights and riding on the pavement.
Police Scotland were unable to provide figures for other former force areas due to different methods of recording the data. However, separate statistics for the number of "reported cycling offences" within Scotland showed a 24% increase from 298 in 2010/11 to 369 in 2012/13.
The biggest increase was in cyclists "carelessly or inconsiderately riding a bicycle", which have almost doubled from 50 to 96. Dangerous riding offences increased by one-third, from 27 to 36, while the number of cyclists caught drunk at the handlebars fell 14% from 44 to 38. The largest proportion of offences - 199 - were simply classed as "other".
Neil Greig, director of policy for the Institute of Advanced Motoring, said the figures would reassure motorists. He said: "I'm pleased to see a rise in cycling prosecutions to match the rise in cycling. Cyclists must exercise responsibility if they want to be taken seriously as a mainstream form of transport.
"For me, it shows that the police are aware of cycling casualties and they're reacting to that. Motorists often feel that cyclists get away with bad behaviour, whether its cutting through red lights or putting themselves at risk in other ways."
Latest Scottish road casualty figures show the number of cyclists killed or seriously injured is now at its highest in five years.
Edmund King, president of the AA, said an increase in cycling would naturally lead to an increase in cycling offences, but that the near-100% increase in Lothian and Borders was "quite striking". He added: "The crucial thing is whether that's down to increased policing or more offences taking place.
"I don't think it's helpful to blame one group or another. All road-users have a responsibility to abide by the highway code, whether that's cyclists cutting through red lights at junctions or motorists texting at the wheel."
The Scottish Government wants 10% of journeys to be taken by bike by 2020. Currently the total stands at about 1-2%, although estimates for Edinburgh put it as high as 7.5%.
John Lauder, national director of sustainable transport campaigners Sustrans Scotland, said: "It stands to reason that as more people cycle there would be more fines issued to cyclists, although it's disappointing. But it is good to see police using the law fully to penalise bad cyclists. Hopefully by doing so we'll see offences go down."
A spokesman for charity Cycling Scotland said enforcement was a key part of making roads safer, together with education and improved infrastructure for cyclists and pedestrians.
He added: "All road users have a responsibility to follow the rules of the road, but enforcement campaigns that help educate road-users on the vulnerability of those travelling by bike and foot are important to helping people feel more confident in travelling actively."