I will answer to the best of my knowledge and understanding on the topic as a fellow Canadian with a bike in Europe. This is assuming you do not have any residency in Europe and are only visiting on a tourist visa. First I will say that the two biggest potential issues are keeping your bike properly registred, and second not running into issues after periods of extended storage. Greencard insurance is available that covers basic 3rd party in most parts of Europe, for the countries that arent covered then policies are usually available at the border for these few countries. UK is trickier since it left EU it isnt covered by most green card policies and seems problematic to get. A few places are able to sell for this, but in general it is quite expensive and not that easy to find. For any of these policies to be legal your bike needs to have current legal registration and in BC where I am from this seems to mean ICBC coverage. It's possible a storage policy might work for this, I havent looked at the wording but basically when your policy lapses then the registration is not considered current. Check your own provinces policy on this if it's an issue. The other is if there are yearly vehicle inspections required for motorcycles in your province then technically this would also have to be complied with and its doubtful that would be possible to do if bike is overseas. Some people do fudge the paperwork a bit, manage to get insurance and pass borders but may not technically be compliant and are at risk in case of an accident. The second issue is that while EU acts as a common zone each country has their own amount of time a foreign vehicle can be inside their borders without being legally imported. From memory most countries are 3-6 months or something along these lines. Since most EU countries have no border checks this mostly applies to EU/UK citizens living in another EU country or leaving a vehicle there for holiday use. Their have been crackdowns in spain for example on UK vehicles that have been in use there for years and now that UK has left EU its more obvious and problematic for some. For North Americans and Australians etc. it seems to be not really a major concern, probably as there are so few of these vehicles in Europe. Many people leave their vehicles for multi-year periods and return to use the bike for a few months at a time and are never questioned. Some of the countries do actually have border checks where they look at vehicle documents and check for green card insurance etc. I think between Greece and Bulgaria this is done and also between Bulgaria and Romania, and Montenegro and some of the Adriatic countries require their own insurance policies to be purchased at the border so when you enter or exit these countries documents will also be checked. Depending on where your bike originally enters Europe you may receive an official temporary importation permit with some specific dates of validity or not. This is all to say that technically there is a paper trail of when the bike entered and left the various countries and by comparing this to your own entry and exits from Europe it could be determined that you were not in compliance with EU temporary importation rules. Practically speaking it seems nobody really cares. You need to present your documents as mentioned at some borders, and basically as long as you have proper ownership, registration and active insurance coverage you should be fine. I took the ferry to Morocco and on return to Spain was only asked to present my passport and no bike documents were needed. So, I can say that for me there is no active Temporary importation documents issued and it is unlikely the bike is in any Spanish or European system. This is most likely the case for people crossing to Turkey and back to Europe.
EU has been talking about activating an ETA visa policy to which Canadians would be subject. As far as I know that has not been enacted yet, but it is possible when this does happen, all of your entries and exits may be clearly visible every time you present your passport to immigration. This could also make it more obvious that the bike had not recently been brought to Europe and questions could be asked. As mentioned up until this point it has not been an issue and it seems that dozens or perhaps 100's of travellers have managed without incident. Most likely none of this is even an issue unless you are involved in an accident at which time the insurance company may use that as a way to avoid covering the incident.