IMO - I guess every one's replies are their opinions, whatever. With your background I'm going to assume you know about notes of the scale 1, 2, 3, 4, 5, 6, 7 and notes within a chord R-3-5 or R-b3-5......... Find a fretboard chart,
Link Removed - the bass fretboard is a piece of cake. Think root note placement and visualize that root's major scale
http://www.studybass.com/tools/chord-scale-note-printer/.
Where is the 5th? Up a string and over two frets. Where is the 3rd up a string and back one fret. Every 5th is up a string and over two. Every 3rd is up a string and back one fret. Where are the 4ths? Up a string and right over the root. I think you've got the idea.
Yes you can teach yourself the bass. An instructor will get you there twice as fast and will help you with technique, but, you can do it on your own.
Reading standard notation - play the notes in the bass clef. Or you can use fake chord or lead sheet music and rely upon the chord names. The following deals with using chord names. Fake chord or lead sheet music is relative easy to come by.
I found
http://www.studybass.com/ to be a very good source of information. Here are some hints of my own:
We play chord tones, i.e. the notes of the chord.
Something like B13(#11) ignore the extensions for now no need to get that detailed at this point of your journey. Focus on what the chord is, i.e. major (R-3-5), minor (R-b3-5), dominant (R-3-5-b7) or diminished (R-b3-b5 - b5 is enough for now). OK B13(#11) for now is just a major chord with some extensions so.....
The Root B will always work.
The 5th degree of the root scale will work with every chord except a diminished chord, and how often do you run into a diminished chord. If you have a diminished chord flat the 5th now it will work fine. A plain ole 5 will work most of the time and is a safe bet.
OK that takes care of two beats. So the root and the 5th are safe bets. With 3/4 time you have one more beat to worry with and with 4/4 you have two more to worry with.
Any other chord tone will work. The 3 is always a good bet. If a minor chord Bm for example use a flat 3, if it is a major chord (B) like the above a natural 3 is in order. OK that took care of your bass line for 3/4 time. If in 4/4 you've got one more beat - any other chord note will be OK. How about an octave 8 for R-3-5-8. Up to you. Use that same
generic riff and change the root as the chords change in the song.
Get yourself some favorite generic riffs like:
Root nothing,
Root -5
Root-3-5-3
Root-3-5-7 or b7 with a dominant seventh chord.
R-2-3-5-6 is the major pentatonic scale and is one of my go to riffs.
Put them into muscle memory and go find some backing tracks and see what you can do with them. Google can usually find something you will like to play over.
Link Removed
It's in E. Which means the chord progression will more than likely revolve around E, A and B or B7. Give it a shot, if nothing else it will tell you what you need to learn. Recap - pick a generic riff for your bass line then listen for the chord changes and move the root of your riff to correspond with the new chord. I think your trombone experience will flow right into your bass. Ask specific questions here.
Let Studybass.com help with what fingers to use, how to mute strings, and stuff like that. Start on page one and bookmark the stuff you need to learn - speed read the stuff you already know.
Good luck.