If that pickup is a BP100, they are hard to get a good sound out of IME. They usually have clips that help secure the paddles to the bridge. Try a google search for images of BP100 and you'll see. Also, even something like a pedal tuner will help with the impedance matching. What amp are you plugging into? Try to find the specs online for the input impedance. If it's below 1m ohms then you might think about using something to help the impedance matching.
When we record, I send a pickup signal, a close mic and a room mic and then the engineer does his magic with a mix of those. The last recording I tried the old "wrap a Shure SM58 with foam and jam it in the bridge feet" trick and it sounded great.
These aren't hard and fast rules. Everyone hears differently and everyone's basses are different, but there are a few common denominators that will help.