Just continue until when? The second E on the E string where the 2 dots are?
Not to make things more complicated, but where would one start if they were on a 5 string?
If you are doing this exercise on a 5-string tuned BEADG, you would start w/ the lowest available note in whatever scale you were working on. If you are doing the C Major scale, that would be the open B (scale degree 7): B-C-D, then move up to E string --> E - F - G .. and so on.
As for the "up one octave from where you started", yes, keep moving up the string until you reach the octave (the B on the 12th fret). So, again as above, you'd play BCD, EFG, etc., only 1 octave higher.
Of course, you can go past the octave and just keep continuing until you run out of frets.