The traditional texts on harmony typically first teach harmonizing with I-IV-V-I progression, dwelling on many technical details - mostly having to do with voice leading. This leaves one with a fairly basic bass line, like those in these examples (image source):
While the bass line is largely "drowned" by harmonically sounding chords, when accentuated or played without tenor and alto voices, it often comes out as plain, boring or even ugly. Of course, the opportunities for bass increase quickly as one starts using inversions and seventh chords, but there seem to be few guidelines for actually writing the bass line (all I have found is that bass follows a "wavy motion", and that in IV-V sequence it moves by a second, and never by a seventh interval.)
On the other hand, counterpoint seems to provide good principles for writing a bass voice (for a novice like me the first species is already more than enough to hold on.) Thus I wonder, whether it could be a reasonable approach to compose first a bass line as a counterpoint and only later fill the middle voices with triads. This would probably mean deviating from I/VI/V - I think with II, VI and first inversions it would be enough.
Is this a valid approach? What are the possible/typical pitfalls to expect: might easily result violating the principles of the tonal harmony? Does it lead perhaps to complexities beyond a beginner's level?