| There really isn't a situation that absolutely does not call for a melodic bass line, although you have to gauge how melodic you want or need to be depending on what else is going on in the music.
A piece of music is like a puzzle where there is no wrong answer, although some answers can sound more correct than others. Two or more players' lines for a song may be radically different but equally effective and musical, and only be different because they're played by different people who hear things in their own individual way. That's where individuality comes in. It's how you put your personal signature on that piece of music and make it yours.
In order to play melodies, you must have a somewhat developed melodic sense. The only way to achieve that is by listening to a lot of melodies and internalizing them and learning to play them. In other words, you have to learn to sing through your instrument. This same principle applies to soloing.
Once you have internalized enough melodies (and this is a process that never stops, which is why we're constantly evolving as players), you'll have a catalog of melodic ideas to draw from, which, combined with your knowledge of chords and scales, will create your voice on your instrument.
Hope that makes sense.
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