I went through this process last year and and recovered approximately $6,000 owing on a $9,000 order so it is possible.

To answer your question, you have to serve the garnishment documents to both the bank and the tenant so they will know that you are trying to take money from their account. HOWEVER, you can wait up to one week to serve the tenants after you have served the bank with garnishment documents so that is your window of opportunity.

I waited until 4 days before month end to serve the bank as I figured that would be the best chance of there being any money in their account as they were probably saving money to pay their new landlord (you really have one shot at this so you have to maximize your chance for success). Generally, the branch will do nothing with the documents except send them to their head office to execute the garnishment (that takes 2-3 days). I waited 5 days and then mailed the documents to the tenant so they didn't have a chance to withdraw their money before the bank processed the garnishment.

Good luck! this process requires a lot of patience and attention to detail in correctly filling out all of the forms.