Like all instrument techniques a lot of it is PRACTICE.
One thing I do when working on my single string accuracy, is to not bother with a melody, just hold a chord (open or fretted), and try to not hit ANY chords with the lead finger (in my case the index finger).
The pattern would be
(1)Single note ;
(2) silence (don't bother with hammering-on or pulling-off) ;
(3) single note (either same one as first beat, or on a different string) ;
(4) Thumb on 5th string.
REPEAT PATTERN ad-infinitum... (do it whilst watching sport on the telly or passing trains or paint drying...)

The main thing about this type of practice is you are learning a pattern which is not specific to a single melody line. Once your brain has it patterned in the skill transfers to any melody where it is needed.
QUACK!
GtD.