I've jumped over 50 now. No dice. Everything is discovered and mapped.
how distant from the bubble are you in your search area? You really shouldn't need to get more than a couple thousand ly to start getting undiscovered systems. The trick is not going towards any nearby nebula or Colonia or guardian sites or directly towards the core as those are common travel paths. And going above or below the galactic plane. try at least 100ly above or below - there should still be plenty density to the stars while in the arm at those distances.
You could just pick star names while viewing the galactic map and have a third party eddb type site open and punch in the names until you get one that is not returning any data ...denoting an area of likely unexploredness and do that method so you aren't spending so much time jumping around just to find out it's not what you want.