Generalized feeling of bad breath along with symptoms of gum bleeding on brushing basically indicate that there a considerable amount of dirt deposit (calculus) on the teeth that leads to bad breath. Other dental reason can also be food lodgment in between teeth which are hard to clean up with brush alone.
Next Steps
I would suggest rule out the dental possibilities first... visit a dentist and get a thorough check up done
if bad breath is due to calculus.. you might have to get an ultrasonic scaling and polishing done and the problem should resolve. if it's because of any food lodgement due to a cavity in between tooth.. a filling should help.