Remove the bearings. There is a light oil made specifically for router bit bearings but most very light oils will work. Just a single drop, then run the bit and bearing on scrap in case oil sheds. Make sure to blow out the bolt hole if you use a water cleaner. Clean the bit as you wish.
My router bits have carbide cutters. I use a single edged razor blade and cut off any build up, laying the razor flat on the carbide's bevel. Carbide is much harder than a razor and it will not even scratch the carbide.=p