The sheet music you describe sounds like songbook music arranged for solo piano or piano and voice. Depending on the range of the piece, it may have one clef or a grand staff, often with chords written above and lyrics below.
The chord symbols describe the harmony of the piece, which helps practiced musicians understand the structure and progression of the song. You can also use the chords to guide improvisation. They do not, however, directly correspond to the melody or bass line.
Typically, the sheet music is divided into different voices. All notes that share a stem belong to the same voice – notes on different stems are different voices. Voices may have single-note lines or multiple-note chords. Simple piano pieces often have a line in one hand and chords in the other.
The lowest voice in a piece is the bass, and when the lowest voice is a line, that is a bass line. Some bass lines are melodic, some harmonic. One especially common sort of harmonic bass line is the pedal, named after the bass pedals on organs, where the bass provides the root of each chord in a steady pulse.
When a line appears in a higher voice, that is more likely a melodic line, although there are other possibilities like counterpoint.