One thing- just remember that there is no "right" way to play bass. Picking is just as good as fingerstyle, despite what some may say...
I understand wanting to be a complete player, that's why I'm trying to get half decent with a pick!
Fingerstyle came more naturally to me from previous cello experience, but I still had to learn to alternate fingers. I just concentrated with slow tempos at first, trying to remember to alternate index and middle fingers. Just kept doing this, usually with one note at first (bunch of good rock songs to practice this with- 8th note root basslines) then doing more complex combinations and rythyms.
*One thing that I believe helped me was actually "walking" my fingers, even without the bass. (then again it may have been more of a placebo effect

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