Yes the bass is generally played with the left hand on the keyboard, when played with 2 hands. I think your question is very general because these rules can always be broken, i.e,. the chords can be played in the right hand and the melody played with the left, but allow me to clarify something.
The bass isn't necessesarily dependent on the hand you play it on but more that it is supporting the harmonic structure of the music. In most music, the bass is the root of the chord (the "C" in C maj, the "A" in A min, etc...) but you can add variation and complexity by having the bass do inversions of the chord by playing the 3rd, 5th, or 7th. This adds different texture and tension to music.
When trying to figure out if a note should be played with your right or left hand on a 88 key piano, the general rule of thumb is that, notes below middle C should be played with your left hand, and notes above middle C with your right. There are of course exceptions to this in certain passages but this should help get you started initially.