Bad smell in mouth

Have you tried anything different to see if it changes? - dietary changes, digestive treatments, etc.? Generally, not always, a bad taste in the mouth is from your digestive system (even if you don’t have any obvious issues besides that).

If by working out, you mean working out in a gym, it’s also possible you are reacting to some of the plastics or rubber in the gym itself. Generally if only you can smell the smell in your mouth (i.e. others don’t think your breath has an odor) it’s somewhat likely to be a chemical reaction, if others can smell it it’s likely to be digestive.