In Australia, there is no law that specifically states that you cannot be breathalysed while riding a bicycle. However, if you are suspected of drink driving, you may be asked to undergo a roadside breath test. If you refuse to do so, or if you fail the test, you may be arrested and required to undergo a further breath test at a police station.
It is important to note that even if you are under the legal blood alcohol limit for driving a car (0.05%), you can still be charged with cycling under the influence if your riding is deemed to be impaired. This means that it is possible to be found guilty of drink driving on a bicycle, even if your blood alcohol level is below 0.05%.
If you are caught drink driving on a bicycle, you may face the same penalties as those imposed for drink driving in a motor vehicle. These can include an on-the-spot fine, licence suspension and/or imprisonment.
So while there is no specific law prohibiting cyclists from being breathalysed in Australia, it is still possible to be charged with drink riding if your ability to ride safely is affected by alcohol consumption. If you are going to drink before getting on your bike, make sure that you leave plenty of time for the alcohol to dissipate from your system before riding.