On the heavy bag you have to learn to move after you hit so you can hit the bag with extended punches. The easiest way to do that is to move to the point where the bag is going to swing to and hit it as it starts to change directions (at its apex). It's also possible you are pushing your punches so the bag is moving more than it needs to (you want the loudest "pop" with the smallest bag movement when you hit). If you move your feet and stay in balance, you can find your punching range. That is really not the hard part. The hard part is finding your range when the other guy is hitting back.

I think the biggest mistake novice fighters make, particularly against taller fighters is that they stay at the end of the opponents jab, in other words in his range out of yours. I think the point of the video is that fighters have to move in and out of range. I agree the wide step is not good, lots of small explosive steps are better. Slipping, feinting and stepping are all methods of closing the gap(I posted a previous question about this). One other point on the video, taller fighters (although I hate you all) have to fight tall, never mind "eye level" if you have a height advantage. Once you get in range, if you are getting the best of it, stay, if you are getting the worst of it, leave.

Range is a challenge that all fighters, no matter how great, have to keep facing every fight. I recently watched Tapia's fight against Barerra (granted it was the end of Tapia's career and he had a lot of miles on him (in and out of the ring)) but the problem was he couldn't cross Barerra's jab and get into range for his left to the body. I then watched Morales against Barerra (which was a war) and I was fascinated with Morale's feints and footwork. He had so many tricks to close the gap...... "Boxers are the world's greatest liars"