Without an instructor I had to find everything out on my own.
My dad was there to help, but I was mostly on my own.
What I did was I just played songs, I'd have a chord chart, music, tabs whatever and I'd just play and play till I perfected that song.
Learning fills, and groove will come from playing songs and picking up from other bassist.
I bought a lot of books with tabbed/notated music in the genres of Funk and Rock and I learned those songs.
Here they are:
http://www.amazon.com/Funk-Bass-Play...0419031&sr=1-8 http://www.amazon.com/Rock-Bass-Play...0419031&sr=1-8
I also had a lot of praise and worship songs on burnt cds, and my dad had charts, so I would listen to those and transcribe the bass line which has helped my ear a lot.
So just playing and playing what your ears like will fit for fills, you'll be able to tell when something doen'st work (I hope).
Later on you can learn music theory to understand why your fill/lick/run works and why some of them don't.
Improvisation is going to come with experience, and later on music theory and playing with other musicians will greatly boost this ability. For now, Improv may just be playing a bunch of licks you have learned, and that's really all it is. Your arsenal increases, and you just play what you feel should be played.
Theory and scales will help make this more defined later on, but just knowing what the root/octave, third, and fifth is can easily make a good groove.
All my improvisation books going into some nasty theory, so you might not be interested in just that, yet.
I'd recommend learning the major scale, minor scale, pentatonic major/minor and your 1-3-5 triads, and extensions (1-3-5-7, 1-3-5-7-9 etc..)
And let that be your guidline for now until you become pretty serious.
Just find your favorite band/basslines, and try to play along and learn the bass line. Either that or play with other people where you have no guidline and it's all your creativity flowing.