My first super rule number one of awesome power and motivation:
Join Talkbass.
Check.
My second rule which almost equals the intensity, truth, justice, and lowend way of the first rule: Ask Talkbass how to start.
Check.
My third and final ultimate rule of power, knowledge, and groove: Never listen to Jimmy Bones when talking about technique or learning pracices.
Well, let's test that one out for completion:
First, pick a genre you like to play in that has a wide variety of bass lines in it. Personally, when I want to feel inferior, I check out some jazz and funk bass videos. Instead, when I want to learn how to emulate a style that isn't way too wicked, I go for some rock and roll.
But, alternately, when I want to practice picking fingers speed, I fret out a chord, or even just a root and its fifth, and I practice bouncing back and forth with my picking fingers. Then I might fret the same pattern a whole step up or down, or even ona different set of strings. after doing that a bit, I start to figure out a small melody or a good quick bassline with it and just keep doing it. Add one or two notes every time you feel you can nail what you were doing previously, and just keep it going.
This won't help your fretting fingers as much, but it will help you start to develop picking/walking speed.
You can try one here that I do regularly (warning, tab attempt ahead):
|-----------------------------------------------------------
|--------9---7---5----------9---7---5----------------------
|--9^7---------------9^7----------------------------------
|-----------------------------------------------------------
|-----------------------------------------------------------
|---------5---5---5-------------5---5---5------------------
|--7^5-----------------7^5--------------------------------
|-----------------------------------------------------------
|-----------------------------------------------------------
|--------9---7---5----------9---7---5----------------------
|--9^7---------------9^7----------------------------------
|-----------------------------------------------------------
|-----------------------------------------------------------
|---------5---5---5-------------5---5---5------------------
|--7^5-----------------7^5--------------------------------
|-----------------------------------------------------------
|-----------------------------------------------------------
|-------9-9-------9-9------9-----9-9----9-9-----9---------
|--7------------7---------7-----7------7------7------------
|-----------------------------------------------------------
|-----------------------------------------------------------
|------7-7-------7-7-----7-----7-7----7-7------------------
|--5-----------5-------5-----5------5----------------------
|-----------------------------------------------------------
|-----------------------------------------------------------
|-------9-9-------9-9------9-----9-9----9-9-----9---------
|--7------------7---------7-----7------7------7------------
|-----------------------------------------------------------
|-----------------------------------------------------------
|------7-7-------7-7-----7-----7-7----7-7------------------
|--5-----------5-------5-----5------5----------------------
|-----------------------------------------------------------
|-----------------------------------------------------------
|-----9-----9-----9-----9--10---9----9----9----9--9-10--9-
|--7-----7-----7-----7-------------5-----5----5--5---------
|-----------------------------------------------------------
|-----------------------------------------------------------
|-----9-----9-----9-----9--10---9----9----9----7--7-10--9-
|--7-----7-----7-----7-------------5-----5----5--5---------
|-----------------------------------------------------------
|-----------------------------------------------------------
|--------9---7---5----------9---7---5----------------------
|--9^7---------------9^7----------------------------------
|-----------------------------------------------------------
|-----------------------------------------------------------
|---------5---5---5-------------5---5---5------------------
|--7^5-----------------7^5--------------------------------
|-----------------------------------------------------------
|-----------------------------------------------------------
|--------9---7---5----------9---7---5----------------------
|--9^7---------------9^7----------------------------------
|-----------------------------------------------------------
|-----------------------------------------------------------
|---------5---5---5-------------5---5---5------------------
|--7^5-----------------7^5--------------------------------
|-----------------------------------------------------------
|-----------------------------------------------------------
|-------9-9-------9-9------9-----9-9----9-9-----9---------
|--7------------7---------7-----7------7------7------------
|-----------------------------------------------------------
|-----------------------------------------------------------
|------7-7-------7-7-----7-----7-7----7-7------------------
|--5-----------5-------5-----5------5----------------------
|-----------------------------------------------------------
|-----------------------------------------------------------
|-------9-9-------9-9------9-----9-9----9-9-----9---------
|--7------------7---------7-----7------7------7------------
|-----------------------------------------------------------
|-----------------------------------------------------------
|------7-7-------7-7-----7-----7-7----7-7------------------
|--5-----------5-------5-----5------5----------------------
|-----------------------------------------------------------
|-----------------------------------------------------------
|-----9-----9-----9-----9--10---9----9----9----9--9-10--9-
|--7-----7-----7-----7-------------5-----5----5--5---------
|-----------------------------------------------------------
|-----------------------------------------------------------
|-----9-----9-----9-----9--10---9----9----9----7--7-10--9-
|--7-----7-----7-----7-------------5-----5----5--5---------
|-----------------------------------------------------------
|-----------------------------------------------------------
|-------9---------9---------------7---------7------------9-
|--7---------7---------7----5----------5---------5----7----
|-----------------------------------------------------------
Anywho, sorry for the sloppy tab. May not have even tabbed it right, since I did it from memory - and I can't indicate note lengths or anyything. If I could write it using standard notation for you, I would.
Another thing that might help you is doing a few exercises to enforce the one finger per fret rule. The easiest one to remember, obviously, is just the major scales. Another one that helps me is this bassline to one of the songs my band wrote:
|-----------------------------------------------------------
|-----------------------------------------------------------
|---5--0--5--7--0--7--8--0--8--10--8--10^12--12--13--12-
|-----------------------------------------------------------
|-----------------------------------------------------------
|-----------------------------------------------------------
|---10--12--10--8--10--8--7--0--5-------------------------
|-----------------------------------------------------------
Then repeat. It's the intro to our song, Hush. Anyhow, this helps with the one finger per fret rule, as well as helping you get used to moving up and down the neck. It can be done across strings too, but this is the way I find most helpful. It also introduces a slide on a non-main fretting finger if done right, which may help you build a callous on that finger.
And finally, I might suggest using a finger exerciser, one of those spring loaded exercise doohickies that provide resistance to your finger to help with finger strength.
Hope this helps and isn't too confusing.
