I don't clean the bore of my .22's anymore. They shoot better that way.
All the old timers at my range feel the same way ... they all stick to rare cleaning of their .22's. the only time a cleaning is necessary is when accuracy starts to go south, many have found that when they do clean their .22's, it takes time to get it shooting well again.
Same goes for running in a .22 ... I just shot a comp with my brand new CZ and then just ran a few dry patches through to get the powder out and that's it. With .22's a policy of little and not very often seems to work best.