RE: One way bearing or just the pull start itself???
Even though it's a bearing, with one-way bearings you want less grease/oil as possible. So yes, I'd definitely try cleaning it. Use some alcohol and paper towel and clean it inside out. This has worked for me several times by simply cleaning it. But if this doesn't work, the bearing is probably going bad and needs to be replaced.
I've also noticed one-way bearings don't like cold weather either. So clean it up and try starting it in a warm environment. And definitely be sure all the screws are securing the pull start to the back of the engine and that the bearing is properly fitted into the bearing slot. And see if that works for you.