If you're in a relationship with an Australian citizen or permanent resident, it's reasonable that you might want to stay in Australia and build a life with them here. Fortunately, genuine relationships are recognised by the Australian government and you should be able to get an Australian partner visa or prospective marriage visa.
The 457 visa exists to help employers overcome local skills shortages. It's a temporary visa that allows a non-citizen to live and work in Australia for up to four years. As an employer, you're responsible for sponsoring someone to work for your organisation in Australia.
An Australian bridging visa is a visa that bridges the gap between your old visa and your next course of action, whether that's a new visa or leaving the country. Like all visas, bridging visas come with restrictions. You might want to temporarily leave Australia while on a bridging visa, but are you allowed?