I take it that you are 'not' referring to the use of a chain drive?it takes me about 5 minutes to get across a galaxy, about to go from the center of one to the center of another. If it takes you more than that, you aren't building very well.
I am not certain how you could do this. The fastest jump ship I have ever built recharges it's jump drive in the time it take for the jump animation to finish. This requires that almost half the mass of the ship be jump modules. It does make for very fast travel, but even this ship could not get from one galaxy to another in the space of five minutes. It takes about 10 to 15 seconds for this ship to clear a star system given normal jump ranges.
I tend to build my battleminers and such with greater than 10% in jump modules, making it able to recharge in about ten seconds. This permits me to move fairly quickly between star systems, allowing me to traverse maybe a quarter of a galaxy in five minutes.
Just what are you doing differently to permit you vastly greater speeds than this?