Taiwan vs Canada
The easiest way would be to hone in a few bikes you are looking at and price compare and also check bike shop inventory as not only is the US/CAN/EU stripped for parts, so is Taiwan! I do not think Canada has an online bike specific website, so you may have to do some searching for local bike shops in your area to see what they carry.
Do keep in mind that if you buy the bike in Taiwan you will have to have it assembled in Canada! Last time I checked, manual labor outside of Asia is 2-3x more expensive! If you buy a complete bike that is 95% already assembled from a major brand (Giant, Merida, Specialized, Trek) assembly fees may vary. Best check your local bike shop pricing. If the cost of assembly off sets the discount you get in Taiwan, might as well buy it in Canada. Sometimes basic assembly is included when you buy from the shop.
Another issue you have to consider is the warranty! If there’s issue a warranty will cover, make sure that it’s a global warranty. If it isn’t, you might be shit out of luck! Do not think because it’s a global brand, warranty is covered everywhere!
If you were to buy from Taiwan, make sure you communicate with the bike shop that you intend to bring it overseas. I would suggest to have the shop remove the bike from the box to make sure there’s nothing missing or any damages. Some extra fees may apply, but personally, I would feel safer knowing there’s no issues with my bike before taking it with me half way across the world.
Shipping in the cardboard box should be perfectly fine as long as it is packed correctly. Do not forget, that’s how it arrives at the bike shop from manufacturers! A fragile sticker from the airline/courier will go a long way.
Current cheapest way is to check it in at the airport. Post isn’t too expensive, but it may take up to a month to arrive. Intl couriers like FedEx and DHL will cost you an arm and a leg since some economy services have been cancelled.
Stuff some of your belongings in the bike box! Don’t waste space!