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EDIT: forgot to mention that the lighter your ship the further you can jump.
This[coriolis.io] is the best build for such jump. You can see from the graph that the furthest jump you can make is 39.98 Ly unless you use synthesis to increase your jumprange.
FTFY. 41.45 LY[coriolis.io]
If you really, really only want to use 3 jumps to cross the bubble though, then if you have Horizons and you're willing to spend a lot of time sourcing the materials for premium boosts, the absolute furthest you can possibly jump in the game at present time is 82.90 Ly (41.45 Ly Anaconda on Premium boosts), that should get you across the bubble in around 3-4 jumps or so. It'll cost you 160 million for the ship, and 1 Arsenic, 3 Niobium (rare), 1 Yttrium (very rare) and 1 Polonium (very rare) per jump though, with the materials possibly taking hours to gather.
If you have about 250k it's easy to turn a hauler into a shuttle that can quickly take you around populated space. Just strip off the weapons, strip off the internals, and fit all D rated modules except for the A rated jump drive. It has 33 to 37 light year jump range depending on how much fuel it's carrying.