If you are not hostile with Hegemony, bribing is the least painful and most convenient way to go to get them off your back. That said, if you want to colonize the whole sector, you probably want to colonize all of the core worlds too, which means killing everyone in the sector... and no more Hegemony to torment you. (Instead, you are constantly tormented by pirates once you are the only one left.)
The biggest obstacle of colonizing the sector is the time needed to farm Ordos after Ordos with Radiants for drops.