All of the above! It's not so much about technique as feel and groove. Sounds like you can groove already, so you just have to soak yourself in the best blues artists' vibes and off you go.
I came from folk-rock and folk-punk, and answered an ad years ago while pro in a touring band. I was thinking 'oh, yes, just turn up on the odd occasion, walk the standard pattern all night and a few extra quid in the coffers'. My education started there, and I actually started to appreciate blues rather than thinking of it as an easy middle ground as so many do.
Mind you, if you can play funky stuff too, you can add further textures which make you as a bass player and hence the bands you play with just that bit different!
Have fun!