Are the strings dirty, greased, muck ridden?
Clean them. Don't boil.
What to clean them with? Well after looking at the ingredients of several successful string cleaners, like Fret Ease's etc.... many of them contain mineral oil. Comparatively mineral oil is relatively cheap if purchased in its natural state.
In other words go your favorite store, go to the pharmacy area and pick up a bottle of mineral oil, it might cost two bucks for a pint maybe. Put some mineral oil on a rag pinch your string go up and down the strings a few times times and it'll start to get squeaky, that's when it's clean. Wipe off with a clean rag.
If you have an old bottle of baby oil that's essentially mineral oil with a fragrance, the fragrance will not hurt your bass string. Use it and your bass will smell like a baby's clean bottom end.
Look for pressure indentations from the frets, kinks over the rollers, nut slot fit, winds on the tuning machine capstan etc...
After the bass strings are all cleaned off and inpected and if they sound okay to you, or not -- then make your decision to purchase a new set -- or not.
Why would mineral oil be found in the pharmaceutical area of a store? Because one of its uses is as a laxative. People actually take a couple of teaspoons of mineral oil to free up the bowel in times of bowel impaction. A couple of teaspoons of mineral oil and perhaps increasing fiber in your diet is all that is needed.
If you want the fragrant blend go to the baby supply aisle.