I advice you to focus on relative pitch.
You're a bassist, so you catch the bass line easily in songs, I don't doubt about that. There may be methods, but I'm just gonna give you some tricks.
Once you feel the bass you feel what is called in classical music the fundamental tone. (I'm french maybe that's not the correct word in english).
When you play guitar or bass, you know that you can always play the fifth at the same time of your bass tone: the fifth it always sounds good. It's called power chord, in french we say 'la quinte juste'/'the right fifth' because it can not be not right. You play an E on the first string with a B on the second, or a G on first string and a D on the second string, an A on the first string and an E on the second string.
This is the ground of harmony. The theory you call for is Harmony.
With the fundamental and its fifth you can add a third note. It makes a chord. Most of the time it goes major or minor. This note can be played as melody to enrich the bass you play.
Once you can easily find your path between the chords that follow themselves in the circle of fifth , you can add notes as adornments: they achieve the real melody/tune.
So before any theory, I advise you to master the cycle of fifth.
And then you'll learn augmented and diminished chords. There are more exotic tunes to experiment further. But learn this circle. It's the base of western music.