One thing that helped me a lot is: Start with a two-beat line. Beats 1 and 3, the most relaxed beats i a 4/4 bar, should consist of chord tones (preferably not too many roots if you think solo). Approach each of the beats with one 1/8-note, then with two, and then with three. Now you have a string of 1/8s , starting on upbeat 3and. On this line, you apply the rhythm of a bebop head you know. Where the head has a rest, you play a rest, where there's a note, you play the note your 1/8note-line tells you to play. Do this a lot on different tunes.
Now, I doubt anybody thinks like this when soloing. This is just a mind- and ear game (one of several) to teach you to always HEAR - and in advance - a two beat line that is dead-on, or right through, the changes (people call it "guide-tones", but "two beat" is a concept any bass player should know and arguably relates to better) on the strong beats, and then improvise the rest, by thinking "rhythm", not so much "notes". I know this Dizzy quote- answering a question what he thinks when he solos: "I fill my head with rhythm!" Once you hear this strong chord reference, you can leave it and re-visit whenever you want to, and since there's always going to be resolution on 1 and 3, chances are it'll all make sense.
An interesting by-effect is that suddenly, there are no hard chord changes anymore.
Don't take my word for it- this is basically one of the things I extracted from Hal Galper's videotaped lessons.
Another cat to check out is Barry Harris and his use of the major scale with an added b13 (well, Donna Lee, anyone?) .
A thing on tempo: Bass players have this thing with always being perfectly clear about the quarter note tempo of a tune, and that is of course great- but it can be a hindrance too. To play fast you have to think slow, is what the olden guys say. How to do that? I practice my uptempo walking lines played as 1/8 notes (still being 1/4s!)- which means that the 2 beat from above is your walking line. So the real 1/8 notes start to feel like 1/16 in ballad or medium tempo (and yes, so you end up with a ballad with a chord change on every beat). Easy, or at least to me, a lot easier than 1/8 notes somehow!
Best
Sidecar