haha I think there are other threads on this, but here's my take on bass improv and solos...
First up this website helped me alot.
http://www.rodgoelz.com/bass_improvisation2.htm
this too.
http://www.ultimate-guitar.com/lessons/bass_lessons/soloing_on_bass_guitar.html
Second, think about the music, and your role in it... for me, a bassist is the link between the rhythm and the melody. so sometimes it sounds good playing only the root note, sometimes it sounds better with a solo.
Third, what you play gotta be in line with the rest of the band.. so you don solo when ur guitarist is soloing, and even when you do do that, make sure both of you are playing something that sounds pleasing to the ears.
but ok that's just some guidelines.
i think breaking it down there's roughly 2 kinds of bass improvs... one is playing leading notes to the root of the next chord, the other is all out solo in the key/chords of the song.
Leading notes
basically you play the notes before or after the next chord. so you "lead" into the note.
you generally want to play the root note on the strong beats i.e. 1 and 3. so when playing 8th in the example below, the leading note (B) to C, B is on the 8th of the first bar, while C is on the 1st beat of the second bar. same for C# to D. C# is on 8th, D is on first beat.
so a simple one will be smtg like...
G-
D-
A-------------2-----33333334-55555553
E-5555555-----------------------------------55555555
Chords: Am C Dm
The following example is one of my favourite song: Hey, by the pixies. Nothing complex, but hey it does a freaking good job.!
http://www.youtube.com/watch?v=PIkWJZf33UY
Solo
errr this one harder to explain here. one way will be to just whack all the notes in the scale in random orders (that sounds pleasing to your ears). that's how I did it
A good example is the solo in war pigs by black sabbath. nothing difficult or flashy, and it's just notes in the scale arranged with some bends and licks, but it does the job very well.
I hope all this made sense, it's rather broad a topic. Ask any questions and I'll try my best to answer them. do excuse any mistakes, headache lah. off to bed now.