In the two years I've been in Korea, I've had two bikes and biked the entire time. My first school was a 25 minute walk from my apartment and the fastest option was biking. I started with a small, red, folding bike and bought it fairly cheap.
My second year, I decided to upgrade. OK, I didn't really spend much more, my new bike cost around 200,000 won, or less than $200, but I was tired of having a little folding bike. I lived within walking distance of my school, so didn't bike as much. But I prefer biking places rather than relying on buses, subways, or taxis.
Now, I live about a 20+ minute walk away from school, again, so biking to work is back on. Plus Chungju is kinda small and it's easier to just bike places than getting a bus (there aren't any subways here) and I'm not a fan of cabbing it everywhere. And I always come across interesting little places when I just bike around for the fun of it.
It's fairly safe to bike, I find that people are much more lax about where you bike (you can bike everywhere!) in comparison to back home. Sometimes there are bike paths, on roads or on the sidewalk, but people generally accept you biking all over the place. Not that it's safe to do that... As per anywhere, you have to be careful and bike like everyone is trying to run you over, and there are a whole ton of scooters all over the place that blatantly disobey every traffic law.
I've been lucky and haven't had any issues with theft or vandalism, and have found it much more bike friendly here than anywhere I've lived in Canada. Bikes are more of an accepted form of transportation. The only thing is, as a foreigner you're already an attention grabber, but as a foreigner on a bike, you get even more attention! My students, middle and university, always love telling me whenever they see me biking.
Even random people around town like telling me when they see me biking. I've been exploring Chungju a lot, by bike recently, and stopped in at a Korean art store the other day. The shop keep, who also happened to be bleeding from his forehead, immediately mentioned/mimed that he saw me biking the day before. Here's my awkward drawing of the guy: