Start with the melody, that's what I tend to do in a jazz solo. It gives the listener something that they recognise. After a few bars I tend to start improvising around the melody/chords. I try to think ahead, having what I'm playing in my head.
Listen to some great soloists, not just bassists, but sax players and trumpet players. Transcribe their solos. I'm a huge fan of Miles Davis, and have a lot of his solos and lines from songs that I play transcribed.