Generally speaking, you do not have to put your bank account number on a rental application. In Canada, there are privacy laws in place that mean landlords can't ask for a tenant's banking information until both of you are ready to go forward with a lease.
At that point, you'll need to pay rent somehow and often that's by post-dated cheque or direct deposit, so your landlord will have some of your banking information at that stage.
Pro tip: on liv.rent, there are lots of convenient ways to pay for your rent.
Learn more:
How to Pay Rent to your LandlordHow To Pay For Rent With Bitcoin On liv.rent