For a bass the blues and the use of a 12 bar blues progression is predictable and because of that you can jam with it in only a few days. Here is an example of the 12 bar blues progression in case you need it.
http://www.youtube.com/watch?v=bUK5p...eature=related
Try - root nothing changing with the chord changes and building a groove. Four beats to the bar. Then......
Root-5 changing with the chord changes is next. Root on 1 and 5 on 3.
Chord tones next, i.e. R-3-5-3 or R-3-5-b7 after R-5 is comfortable.
Here is an easy one, it too is in A, remember the progression is predictable.
http://www.youtube.com/watch?v=cM2G1...eature=related
A "fancy" (or expanded) 12 bar blues progression moves quickly into jazz. The chord charts for jazz standards are easy to find. Since you are coming from sheet music move first into lead sheet or fake chord sheet music - I think that will ease the journey. What type of music beyond blues and jazz? Whatever you like. Pop music is basic three to four chords and hang on.
Here is a paper on the evolution of the 12 bar blues progression.
http://www.bobbrozman.com/tip_evol12bar.html
Fake chord and backing tracks on jazz standards
http://ralphpatt.com/Song.html
Notice the backing tracks button in the tool bar.
Once you have the chords for the song how much of the chord (root only or R-3-5-b7) you use in your bass line is pretty well left up to you. The beat or groove will govern how much is needed. Coming from by rote playing I think you will enjoy the freedom of composing your own bass lines.
This may help.
http://pagesperso-orange.fr/freebass...20Redding.htm#'' Pain In My Heart ''
Scroll the screen down - help yourself to some standard notation bass lines.
Jamming is great fun.
P.S.
www.studybass.com is a site I think you will like.