How long does it take to get your bachelor's degree in sports medicine when you already have an associate's degree in massage therapy?

It depends on exactly which courses you have completed at the associate level, and how they fit in to The Bachelor's degree. When students finish the associate degree within a transfer program, then transfer to a four year institution within the same major, it typically takes an additional two years. However, in your case this is not a transfer program, and I assume it is an associate of applied science degree. Thus, I would imagine while some courses would transfer, there will be few that do.