Many things can cause halitosis (the medical term for bad breath), and one of them does involve your nose, although that is not necessarily the cause in your case as you don't mention any sinus symptoms. The nose and the mouth are connected to each other, as you undoubtedly known from snorting water up your nose accidentally. Your nasal cavity extends straight back to the base of your tongue, with only a thin palate separating it from your mouth. Any bacteria that are present in the mouth will also be present in the nasal cavity, as they are in continuity and are lined, at least in the back, with the same type of mucosa (which is why the smell can be present through your nose).
That being said, most cases of bad breath start in the mouth. Improving oral hygiene and gargling with mouthwash can help in these cases. Postnasal drip can sometimes fall onto the back of the tongue and create a bad smell as it rests there. Nasal causes are the next most prevalent, but are usually less than 10% of all bad breath, sometimes described as being more "cheese-like" in quality than other sources. Nasal saline irrigation can be beneficial in cases of chronic rhinosinusitis, and an allergist or otolaryngologist
would be able to help guide you with further treatment options. He or she would also be able to tell you if a polyp or other obstruction is adding to your problem. Tonsils and other sources can, infrequently, trap food particles and cause bad breath as well. If your problem continues to aggravate you after these attempts at correction, please see your doctor