1-2 wraps is more than enough for a B, 3 wraps is a bad idea. 3 wraps is more appropriate for an A string.
The low B is am extremely thick string so you cannot hit it with the same force as an E, especially on an EB, their low B is kind of sloppy in my experience. Playing at the bridge will allow you to hit harder and faster but it will not give you the ticker sound you are after. Don't use your thumb either.
I also wouldn't suggest major adjustments to anything until you change strings, otherwise fresh strings will pull everything out of whack. Are your pickups unusually low on the B side?
Just remember, you don't have to assault your bass to make it sound big, play light and EQ in a thunderous sound. You have to EQ down a hard hit, to remove the clank, a light touch can be EQ'd massive on record.
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