A technique that allows you to play fast music on the bass is two finger alternate picking.
To start practicing this technique, take your index and middle fingers on your picking hand, and just start picking any string while alternate between the two fingers. Pick with the index, then the middle, then index, then middle, etc. You can also start with the middle finger too.
It doesn't really matter what finger you start your alternate picking with. Try both, see what feels natural to you, and stay consistent with your choice while you practice.
Here are three alternate picking bass exercises to help get you started:
For more detail on approaching alternate picking please check out the following video:
Got any questions? Please let me know! Video suggestions are always welcome too.
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John Taylor - guitar and bass instructor for Mile High Shred.