It sounds like the problem isn't strength so much as your shins hurting when you hit the bag. The pain will get better if you keep hitting the bag several times a week to the point of discomfort or mild pain, but stopping before severe soreness or severe pain. You'll get used to the feeling. If you only go to class once or twice a week, an additional home workout or two is called for.
I'd make sure to do heavy barbell squats, deadlifts, lunges, and farmer's walks in order to increase bone density, strength, and overall resistance to injury. That will help make sure that the shin pain doesn't develop into real injury. Once those are in place, I suppose sprints, jumps, and other forms of high-impact supplemental training could help.