Besides working the bags with heavy gloves, and light hand weights, what are your favorite/best exercises or drills to build shoulder endurance?
Weights: Lateral Raises - These worked a treat for me, as my endurance was bad (the shoulders are only a tiny muscle-group, hence why they can tire so quick). Non-weights: More rounds on the pads, more rounds spent shadow-boxing, more bag work, More combos.
Resistance band punching. And get a double end bag, kind of tight and stand back enough to where you get full extension and throw straights as fast as you can, I throw it in when I'm circuit training. Do it for multiple full rounds.
How many reps or how long in time? I imagine you use light weights... NOTE: looking for things I can do outside the gym 2-3 days a week besides sparring, bags, mitts
You don't need endurance in your shoulders, punch more with your legs/torso and your arms won't need to do much work. You should be looking to get your shoulders strong to be able to absorb the forces without getting injured.