YES!!! Travel insurance is always a good idea, even if you're not planning to launch yourself off 50 foot drops. The cost per day is negligible and you never know when a wicked little root, an unseen rock, or a rabid squirrel will cause you to crash. While the medical system in South Korea is excellent, long-term medical care expenses can add up quickly, and being repatriated to your home country can literally cost a fortune. When looking at insurance options, make sure you choose a carrier that covers "extreme" sports such as mountain biking.
You will also need to sign a waiver before either renting a bike or joining a tour. Feel free to print out and complete the waiver before you meet your guide.