Well, you've asked the million dollar question in Elite. It gets grindy and there's not exactly a bunch of options. You will get higher payouts the more you increase your rep with a faction/system, a.k.a "grinding missions some more."
If you have a Cobra you can keep on hunting those pirates "adequately," but if you want to feel like you have teeth then grind your way into a Vulture. Then bounty hunting becomes a little more exciting as you can actually take on bigger ships like Dropships, Pythons, Anacondas, etc in nav beacons or hazardous extraction sites (still helps if you have help, though)
If you want, get involved in the Community Goals that appear on the map. While also grindy, if you play in open, you will have more interactions with the community there than just bouncing around random systems trading and fighting NPCs.
Exploring, passenger missions, and mining are slow, peaceful, yet also grindy options. Trading can be more exciting as you'll get interdicted more often, but while the Cobra *can* trade, you'll be better off trading in an ASP or buying a tank like a T6 and outfitting the best hull/shields you can afford on it.
Unlocking engineers to improve your ship's modules is debatably the most grindy thing in the game. A lot of people hate it, but it's also there for you as an option if you want to farm bunches of material for fairly small increases in power, distance, output, etc. on weapons, shields, engines, etc.
Basically, there will come a point you'll need a break from the game. I took nearly a 5 month break from it last year. But I still come back to it. Part of me wishes you could have multiple character slots so when I'm 20,000 ly from civilization exploring, I could jump to another character in the bubble to do some bounty hunting.
