You might be right but rather than being a bully be a helper and convey your message with some polite attitude and it will will strike even better.
No, I didn't bully him, I was just letting him know that he didn't stand a chance if he continued what he did. I agree that the spoken language may differ from the text we regularly read, but when you provide a service, you have to show professionalism on your part. If even the most basic thing you do is violating, what are the factors for someone to trust and hire you 
I don't understand why you use the word "bully" here, I call that comment in the most honest way 
