Assuming you're FED, I play in Andhrimi system. It has a shipyard, couple of RES within 500-600ls and very close to the Empire border so I can claim the Empire bounties too. I've tried other places for bounties but the spawn rate was too small.
Definitely go to a RES and stay within 5KM from the center of it. Look for the kind of ships you get, if you see Anaconda, Python or Imperial Clipper, you've hit the jackpot and you are in a good instance. If not, exit to SC and re-enter.
Do not attack until you scan with the Kill scanner, I've read it may double the bounty. Since I always use I can't confirm or deny.
Don't try to take an Anaconda by yourself in an Eagle. Make sure you have a few authorities around you before you attack, and preferably do not attack first. You can scan with the kill warrant before that and then just wait. The scan persists until the target is destroyed.
For the first few sorties, Sidewinders and Cobras are still fine, you will rack up the bounties to 2-300k in about an hour or two then you can upgrade to better ship/gear. I've used weapons with no ammo exclusively at first to maximize the profit.
Good luck!