My Intruder 800 went 135,000 miles on ther cheapest, no-name car oil I could find on sale. My 'new' Intruder has 85,000 on it already, also using whatever cheap, no-name car oil I can find on sale in bulk. My Electra Glide is pushing 60K already, never seen a drop of synthetic. I have lost track of how many miles are on my shovelhead (I always put in a fresh odo to keep track of when it is time to do the top end) but it probably has 250,000 on it, and has never seen a drop of synthetic either.
Run the correct weight of oil, change it and the filter frequently, and use whatever type of oil you want. As for switching to synthetic, should you decide you want to spend the money on it, you can do it at any time. Semi-synthetic oils are a blend of conventional and synthetic in the same bottle, so there are no issues with mixing them in the same engine.
Car oils with friction modifiers will make a wet clutch slip, most noticably with a high horsepower engine. I have put one quart in my Intruder while traveling just to top it off when there was nothing else available, and the clutch slipped immediately and continued to do so until I changed the oil. A guy here put car synthetic in his Cavalcade, and could not get the bike more than a block from home because the clutch was slipping. He changed it to motorcycle oil and no more problems. Your C50 is not exactly a torque monster, so yo may or may not have this problem.
The wet clutch also contaminates your oil quickly, as it sheds friction material into the engine oil every time you use the clutch, so no matter what oil you use change it at the recommended interval. The viscosity may not break down, but synthetic still gets dirty and full of acids, so just because the viscosity is fine for three times as long does not mean you should keep it in your motorcycle with a wet clutch for three times as long.