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I read somewhere that the bass line is usually the tonics of the chords in the progression. But I doubt this is right.

So if we're playing a bass line, is the current bass note just one of the notes of the underlying chord? So if we're playing a C major chord, then the bass note can be C or E or G?

Or can the bass line just be any diatonic note regardless of the progression?

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I read somewhere that the bass line is usually the tonics of the chords in the progression. But I doubt this is right

If you did a statistical analysis across pieces of music that feature an identifiable bassline and an identifiable chord progression, you'd certainly find that the bassline is playing the root of the chord a lot of the time. Whether it would be 'usually' - as in, more than 50% of the time - I'm not sure. Some basslines mostly stick to root notes, some mostly stick to chord tones, and some basslines use lots of passing notes which aren't necessarily even restricted to the diatonic notes - walking basslines in Jazz are an example, but there are lots of examples where rock and pop songs do this.

As suggested in Bass line melodies, a bass line doesn't have to serve a chord progression at all - it can be the centrepiece of a song, with other elements working 'around' it. Often songs of these type don't have a clear chord progression, even though the motion of the bassline and other elements still gives a sense of motion in the harmony.

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A bass line does whatever it needs to for a given piece. The first line you said holds weight, but is an oversimplification of its role in a piece. The job of a bass line is to define the harmonic and rhythmic structure of a composition.

Just playing the root of a given chord gets the job done harmonically, but it almost is never the best way to make the bass line flow which is very desirable in most styles. There's also the possibility of the bass being completely a non harmonic tone and just stay on one constant note known as a pedal point or drone. What kind of line is needed and which one will fit best will depend on the piece itself.

There are many ways to expand on playing beyond just root notes. I won't go over them here, but you can see this answer for a few basic ones.

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