You can develop your skills in learning how to play piano without having to use a bass line. This is true, especially if you're playing the keys with a bass player in the band. You certainly do not want a battle going on between the keyboard bass line and the electric bass line.
Have you ever heard a musician use the term "Pocket"? A good "pocket" is achieved when the rhythm is playing together and establishing a groove that is soothing. Each musician is functioning in their roll in a tasteful non-abrasive manner and not competing and playing over each other.
So how do you develop this skill? You have to gain an understanding of left hand chord voicings. These are chords played in the left hand that are rootless. The term "rootless" means that there is no bass note in the chord. Playing this type of chord voicing will allow the bass player to play the bass notes and free the keyboard player to improvise or create more intricate harmony with the right hand.
Contemporary musicians usually play these chords using sevenths, ninths, elevenths, and thirteenth chords. All the chords for the right hand can be played with the left hand. Here is a diatonic chord exercise. For example, in the key of C major there at eight diatonics derived from the C major scale.
C maj7= C/B E G
D min7= D/C F A
E min7= E/D G B
F maj7= F/E A C
G add2= G/G A B D
A min7= A/G C E
G/B= B/G B D
C= C/G C E
Notice that each chord is spelled out with the root. When you practice these chords only play the right hand portion. For example when you play the Cmaj7, only play B E and G. The C is played by the bass player. These chords will also serve as substitutions for your major and minor triads. If you normally play a Dm chord, play a Dm7. The 2-5-1's in both major and minor keys should also be practiced in the left hand.
Jazz piano chords played as rootless chord voicings give that open, airy sound that I love. For further study of rootless voicings visit