Running vs. Bagwork for a 45 year old sparring partner

[mozilla2004]

I want to improve my conditioning and endurance for sparring in gyms. I'm not actively competing in the amateurs. But for the past 20 years, a coach from a nearby boxing gym will ask me to show up once every 3 months to spar some people he's training to get them ready for some local city tournaments. i'm trying to figure out whether running is suitable for me to improve my conditioning, and hence be a better sparring partner to my young friends entering the sport of boxing.

I've never taken my running seriously. Even when i did compete in the amateurs, all my other team mates could run effortlessly longer distances than me and faster than me. And all my past coaches never seemed to emphasize running either, they just used running as warm up. When I run, i can only go a little over 2 miles. It would take me about 16 minutes to cover 2 miles. In the first mile, I would sprint 30 seconds then moderate jog for 60 seconds, and repeat the cycle 6 times. In the second mile, it's mostly a slow jog. I would feel pretty tired after those 2 miles.

When it comes to bag work, I have a similar sprint session. In the first 9 rounds on the bag, i'm working at an intensity that feels like a slow jog (6mph), and i'm mostly focused on working a technique/routine I want to use. i move around the bag a lot, so im not stationary. In the final 3 rounds, I punch all out for 30 seconds, then relax punch for 30 seconds, and repeat this cycle for the rest of the round. In the final 3 rounds, I'm trying to simulate the exhaustion I feel when I have to fight someone very aggressive who wants to bang for 3 straight rounds. I only get 30 second breaks between each of the 12 rounds.

So my question is: Is running worth it for me? Or is something like the final 3 rounds of my bag work pretty much the same thing? Or is there something I should modify to my running to make it better than the bag work?

I am currently 45 years old and have a full time job in an office. I can't do boxing and exercise 8 hours everyday. I'm trying to be smart about where I put my time into improving my conditioning to a point where I can still be a useful and challenging sparring partner to my younger friends who are competing.