I liked the ones they came with. They lasted a really long time, and I didn't have your B string experience. I replaced them with a set of DR black coated strings (forget which ones they exactly are) and oddly enough wound up with B string problems. I think quality control on all strings leaves a lot to be desired. The Fender B was clear, tight and defined - the DR string dull, lower in volume and a lot less defined.
The stock strings are Fender Super 7350-5M Stainless Steel (.045 to .125). Last time I tried to find them they didn't exist though, and I had to buy a 4 string set with an added B. Might want to just try replacing the B on yours.
www.juststrings.com
PS. Switched to them stock fender strings on my other basses and I'm very happy about it. Used to use DaDarrios.