Learn melodies to all songs and play them. Listen to all great players of melodies and emulate their feeling and timing. The swing era is full of them: Artie Shaw, Benny Goodman, Pres, Armstrong. Practice playing the melodies as if you were the lead alto in a sax section. Make it swing and have rhythmic vitality. Get someone to provide a Freddie Green-like accompaniment. Most bassists can't flash out like a sax player so don't. Start with the melody and move on from there. Try to make your soloing a sound like a clean presentation of a "head". AND/OR work on 5-note groupings, diminished patterns, extended techniques and pentatonics.