Pay attention to where exactly in the system you are when you receive the bounty. Although an 'anarchy system' is for the most part lawless, bits of the system might be controlled by other factions which do police their space. The specific ring you are showing here shouldn't trigger any normal bounty as it is clearly lawless space.
The bounty you are showing, however, is a powerplay bounty. I don't think regular jurisdiction has any bearing on those, you get them purely for taking part in hostile powerplay activities. They shouldn't have any consequence as far as station access and the police is concerned, but they might allow players aligned with an enemy power to attack you legitimately. Mid you I don't take part in powerplay so I haven't kept track of how this works for a long time.
