Chords are just several notes played at the same time. So that G7 in your exercise: the G7 chord has the notes G, B, D and F (if you're asking why, that's because if you changed any of the notes, it wouldn't be a G7 anymore, it would be a different chord; the G7 sound is actually defined by the notes G, B, D and F put together). And if I play them all at the same time, like on a piano, I get that very specific G7 sound. Now, you can think of arpeggios as really just chords played one note at a time. So on your bass, if you play G, then B, then D, then F, (i.e., NOT all at the same time, but instead one by one) what you did is arpeggiate the notes of the G7 chord - but we now call it a G7 arpeggio because you played it one note at a time, "bottom to top" starting from G and ending at the F. There really isn't any trick here, so if it feels like you're missing something, you really aren't (from a practical perspective). Arpeggios are chords just broken up into pieces, and chords are arpeggios played all at once. Make sense?
Now as far as scales go, that gets a little more complicated because names of what are called modes get involved. The scale that is typically taught to accompany a G7 sound is called G mixolydian. If that name sounds scary, that's totally fine; I normally don't teach students modes until they're well acquainted with chords and arpeggios first, and then the major and minor scales (I'm aware most teachers tend to teach them earlier than that). As far as playing bass goes, it's far more important for you to become acquainted with your chords and arpeggios first (and be able to know all of the chord tones of any given chord, or figure them out) because a good jazz musician "knows all of his/her changes," i.e., knows their chords and arpeggios inside and out.
As far as basslines go: They are, out of necessity, mainly constructed out of chord tones because the bass has the task of both describing the harmony as well as keeping time. If you're new to playing jazz bass and you use that G mixolydian scale on that G7, you could make it sound like a whole bunch of other unrelated chords and could cause confusion to the other players on the bandstand. However if you play that G7 arpeggio by itself, absolutely nobody will be confused as to what chord you're playing (even if a plain G7 isn't super interesting to the ear, it's still 100% right). That's in part why arpeggios are so important for building basslines. After you learn your arpeggios (and chords) you can start creating more interesting basslines by adding other stuff to them, like approach notes, passing tones, scale tones, and so on. I hope that clears it up a little.