My suggestion is to start with the left hand going while you learn.
If you learn to play with only the right hand first, one of two things will happen.
1. You will never learn to play the left.
2. you will have to re-learn all over again how to play using the left hand.
You are already a musician, so that is a big plus. My suggestion is to find a tune that you can play to some extent on the left side and slow it WAAAAAY down. Painfully slow so that it's not even noticable as a song.
Since you are a musician already, you know where the bass notes are supposed to go, it's just a matter of getting them there!
Try taking just a little piece of a song and play it over and over with both right and left hand going, start really slowly so that you can play both sides at once. Then speed it up little by little.
Once you start to feel and hear the relationship of the bass side to the melody side, it will start falling into place.
I used a "muscle memory" left hand training method. Load the CD player in your car with Cajun tunes and as you drive 'play' the base-chord left hand part on the steering wheel. Pretty soon your left hand will be tapping base-chord automatically to every bit of music you hear. It sounds strange but it allowed me to concentrate on the right hand when learning a new tune.