Relaxation is my best advice!
I've been doing rounds on the bag and it has been gassing me pretty quick. What I found is that I'm able to work longer and have more oxygen the more I just relax and let the technique and body mechanics do all the work instead of trying to power every shot. For a 1,2,3 combo, for example, I was hitting the bag with a BANG......BANG......BANG! Now I just bang, bang, bang, it's hard to put into words but the quick combos and resetting back to guard just as fast seem more powerful overall than those muscle shots!! Don't get me wrong, when the opportunity presents itself the "BANG" punches pack quite a whollop and they do have their places but overall you're setting yourself up for more fatigue and leaving yourself open for a counter punch. Make sure to sharply exhale on each punch too, with a 1,2,3 combo your exhale should sound like an "ish, ish, ish" not a "shh......shh......shh"!
My next piece of advice is if you're chasing the bag around then you're doing something wrong, learn to control how the bag works and don't let the bag control how YOU work!