Formal way to wish good morning

I agree with trex279 that "I bid you good morning" sounds very old fashioned and is overly formal in most cases. If you want something more formal than "Good morning", you could try adding the person's name ("Good morning, Mr/Mrs [name]").

I believe the most widely accepted formal way to bid good morning is just to say "Good Morning"."I bid you good morning" is a bit too verbose, and archaic.

Not an native English speaking person, I have lived in the southern US and in Canada and therefore would propose "good morning, sir" and "good morning, ma'am". This works especially well by the way if you forgot a persons name, is very polite and uplifting. Don't try it in New York though, unless you want to provoke an outbreak of amusement. ;)