If you want to develop strength in your LH, then practice the exact same thing that you do with your RH. So, if you practice major scales in your RH, then practice major scales in your LH. If you play chords in your RH, then play the same chords in your LH.
Also, if you want to effectively run a bassline, then you have to practice it. Fingerings are different for every key, so it don't do you no good to just learn it in one key. You first need to figure out the notes of the bass line you are trying to play. Then, once you have the notes, come up with fingering that will allow you to play that bassline smoothly for a long period of time, and at any speed. I'll give you the basic shouting bass line w/fingering in the key of Eb, but you have to figure it out yourself for the other keys.
Key Eb LH/RH
Eb = index finger
G = pinky
Ab = middle finger
A = thumb
Bb = middle finger
C = thumb
Db = middle finger
D = thumb
(repeat)
Eb = middle finger
F = thumb
Gb = middle finger
G = thumb
Ab = index finger
C = pinky
Db = middle finger
D = thumb
(repeat)
First, practice this at a very slow speed. Many people can play a bass line fast, but few people can play at a slow speed and keep it up. As you get comfortable with it at the slow speed, gradually increase speed until you get to where you want to be.
Once you are comfortable running a bass line, then try adding some RH chords to play while running your bass. You can start by alternating minor 1 and minor 2 chords in the key you are in.