Have you taken you bass to a luthier for a setup since you got the bass? Many times a soundpost adjustment or replacement can make a huge difference in the string balance.
Since you are new to doublebass, you may simply not pulling the strings hard enough or evenly from top to bottom. Pickups that are located close to the strings do not accurately reflect the true acoustic sound of the instrument since the pickup "hears" more of the string than sound from the body where most of the acoustic sound is produced. Even though you have many years of experience in playing electric, the touch on a doublebass is different and it takes a while to build up your hands. You might consider taking a few lessons from a good doublebass teacher. If for no other reason than preventing yourself from developing bad habits that you will regret latter.
Welcome aboard and good luck.
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95% Retired Midwestern Luthier
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