If your focus is improvisation, then I recommend you start by practicing:
- a simple chord voicing in the left hand, and
- a simple improv technique in the right hand.
It's fine if you can't initially play both hands together (most people can't). Start with your left-hand voicings first, and practice these alone until they become automatic.
Voicing in the left hand
For your left-hand voicings, start with Bud Powell/shell voicings, and then move to rootless A and B voicings. Shell voicings contain only two notes: the root + either the 3rd/10th or the 7th of the chord. In a ii-V-I, you switch between the 1-3 voicing and the 1-7 voicing. Practice both voicings for each chord. This might require playing through the recording twice, switching every chorus, etc.
Improvisation technique in your right hand
For #2 (improvisation techniques), try these:
- playing a single chord tone (e.g., the 3rd, then the 5th, then the 7th, etc.)
- approach a single chord tone (same exercise as above, but approach the tone from a half step below, a scale step above, or some combination of both)
- playing chord arpeggios followed by scale runs
- playing scale patterns
- finding lick you likes from a recording, transcribing them, and practicing them over the blues in all 12 keys
Improvising solo piano in a jazz context is ultimately a mix of many different skills. The left hand alone has many different techniques you'll ultimately want to master and have at your disposal while improvising with your right hand. My recommendation is to start with a smaller group of skills (like the list above) and making progress on those before moving on. In solo jazz piano, it's easy to overwhelm oneself with trying to learn too much at once. Walking a bass line is something I'd recommend doing later. It tends to be less used in an improvising/soloing context, and it's much more difficult to achieve independence between your two hands.