The pirates you’re hunting can be three systems away from the planet where you got the mission, not two. And it appears their location is pre-generated and they don’t move, so if you never enter the correct system, you’ll never find them. This also means that if you load up on bounty missions, the odds that you’ll run into multiple pirate fleets simultaneously goes way up. When that happens in a system that already has a high chance of random pirates, like Shaula, even a fleet of Shield Beetles can be overwhelmed unless you draw them far, far away from the planet and the incoming hyperspace routes. (pro tip: the “hold position” key can be applied to single ships by selecting them, not just your entire fleet)
[Mac version 0.9.6, based on a small Perl script that does a crude scan of the save file; haven’t figured out how they mark missions as completed yet, though]
The game is free, fun, and desperately in need of a nicely-designed PDF with all the obscure keyboard shortcuts (scattered documentation here, here, and here). You can also get it on Steam for convenience (no DRM applied, because GPLv3).
It’s moddable, replayable, and regularly updated, and doesn’t chew up a lot of resources when paused, so you can easily hop in for a few quick turns while waiting for other tasks to complete. It auto-saves every time you land, and it’s quite stable.
Speaking of free games on Steam, the ancient MMO Anarchy Online showed up there recently. They’ve been trying to get me to come back for about 15 years, and this time I decided to give it a shot. I managed a successful password reset on my old account and created a new character (the old ones were still there but marked “inactive”), and got the dubious pleasure of remembering what it was like before MMOs settled on some basic user interface conventions. I could adjust to the low-res models and textures, but the controls are another story.