If you like roundwound strings, try Fender "Super Bass" nickelplated steel strings.
http://accessories.musiciansfriend.c...ngs?sku=101297
They're very inexpensive, but very, very high quality! My Peavey Axcelerator 6 is 35" scale and they fit without a problem, remember, many Fender basses have string through body so they make them longer than some string manufacturers.
If you're concerned about scratching the wood on your neck, look for Nylon Tapewound strings. Unfortunately, they are very expensive pretty much everywhere.

I love LaBella Nylon Tapewound strings on my Brice.
You may not get much better "B" string clarity even with better strings. The problem may be in the cheap bass. My Brice has a floppy and vague sounding "B" string, especially compared to the snappy perfect "B" of my USA Peavey.