As a noob bassist, I've been trying to graduate away from the single right hand finger to using two. I think I'm getting better, but it's still frustrating at times. Often times my brain gets confused about which finger to use and they trip over each other. Especially if I try to go too fast. Or else I inadvertently mute a string with one finger while trying to pluck it with the other. That's fun.
So what's a good way to get proficient? How can I train myself to use two fingers effectively?
I spent a lot of time working the kinks. It's pretty easy to alternate between fingers using one string, where the main issue enters is switching strings and making it smooth.
What I did to make this seemless was I played 3 notes on one string alternating fingers, then switching to the next string not using the finger that played the last of the three notes. Start on the E string to A to D to G play the three notes on the G then reverse the process. Three more notes on G then D-A-then 3 notes on E then reverse starting with three more notes on E proceeding to the next string.
The reason I use 3 notes on a string as opposed to 4 is if you go through the whole process, you will find you plucking finger when switching will alternate when you reverse.
What else is important is as you build up speed, to get your left hand coordinated with your right hand, I alternate the fingering with my left hand at the same time using a three fret chromatic scale.
There are some other skills you will need to master, like when to rake, slapping and such, but in general I can't begin to tell you how many hours I spent 40+ years ago developing my technique using this method. I still use it today especially if I haven't been playing much. I encourage you to take this seriously as boring and as mundane as it may be, but it is a great time investment.
Best wishes. I hope this helps.