First and foremost, there is a law that bans motorcycles from entering the freeways. If you decide to try, I'd recommend you go on the non-toll gated motorway and not the tolled roads. I've heared stories of how the police will infact block off the entire highway to stop a biker. The good news is that this is almost the only case in which the police will mess with you if you're on a bike.
If your bike "looks" beefy, the police won't bother you for the most part. Motorcycles are largely seen in a similar category as pedal bikes so they're mostly left alone. You will most definitely be bothered for a stop if you are riding around town without a helmet. I have seen many delivery boys and heard of many foreigners who have been pulled over for not having a helmet. You will more than likely only receive a warning the first time, but since you're probably a foreigner reading this, there's a good chance they'll remember if you get pulled over more than once.
Now, getting back to the cops not bothering you. I'm just saying, don't tempt fate. Don't go swerving through traffic at 200 km/h as you pass a police officer because if you tick one of them off bad enough, they will come after you. That being said, there is a basic understanding that so long as you're not riding like a complete idiot, but are riding in a "safe" manner at 160+ km/h (100mph) most cops won't bother chasing you. Also, one of the best things about riding in Korea is that the police rarely do traffic patrol and most speeding offenses are enforced by speed cameras that will take a picture of the front of your vehicle and bikes don't have front license plates.
What it all boils down to is the amount of respect you show. A lot of people look at these dumbass delivery boys on their 125 cc bikes running red lights, filtering through traffic on local roads at full bore, making turns around blind corners and think that it's okay to ride like that. You will hear a lot about people who die on motorcycles, the majority of people who die on motorcycles are these dumbass high school student delivery boys. Yeah, you won't get a lot of mess from the law if you decide to ride like this in urban areas, but just use some common sense. You can still enjoy all the speed and exhileration that riding a motorcycle has to offer by leaving town and finding less populated areas and country roads. I'll dicuss finding such roads later on.
There's a rule of thumb when riding in America and that is to see everyone else on the road as a potential enemy and to expect them to try and "get" you. That rule is even more important in Korea. I mean this to the greatest amount of offense as I can inflict upon drivers in Korea, LEARN TO BE A LITTLE MORE AWARE WHEN DRIVING. I have never seen so many people just blindly shove half their car into the lane when coming out of a driveway, not looking before crossing intersections, ignoring stop/yield signs, oh, and don't even get me started with the number of people who will randomly swerve over the median on cell phones. It all works if you're Korean and grew up driving in Korea or India or China or one of these countries where traffic laws don't have as much meaning, but if you grew up driving in America or Canada you're going to have to be a bit more aware of the sheer stupidity that you'll encounter from the drivers here.
I don't want to say that I condone speeding and I don't want to say that Korea is lawless. The fact of the matter is that the police here are seen as a preventative measure for violent crimes, as it should be. Although I can feel that the "police state" is coming to a rise, it is still somewhat lax here and bending the law a bit will not get you into as much trouble here so long as you're not endangering others.