Hello!
There are many causes of bad breath (halitosis). Most common cause is poor oral hygiene. Apart from that dry mouth (xerostomia), your dietary habit, tobacco or alcohol consumption,
diabetes, gastrointestinal dysfunctions, respiratory infections etc. may cause it. You have mentioned that you don’t have any dental problems and when you burp you smell the food you ate hours back then it might be from other origin. But we could not rule out the oral causes without detailed examination. Please visit your dentist. If he/she didn’t find any oral origin then he/she might refer you to a specialist.
Thank You