Space isn't just about less notes, but being strategic in where you play them, where you play rests (a rest is not the same as simply not playing, it's intentional space), and understanding when and how to use different note durations.
A great exercise to work on this is giving yourself a certain number of bars, in which you can only play so many notes. Note notes as in pitches, but notes as in making any sound come out of your bass.
The most basic level is: 2 bars, 3 notes. Sure, you can throw three big fat notes into the first 2 beats, but then you have a pretty long empty space afterward. If it's too open-ended you can refine the exercise a bit, give yourself a half note and two 8th notes, or whatever combination makes you approach playing from a unfamiliar angle.
Rather than barfing out a thousand notes all at once, you'll start to appreciate each note, and how the space between changes the next note's impact. You can add more bars, more notes, more restrictions, or even just practice it over various changes. In the end, the goal is to get comfortable crafting bass lines that have few notes and still get the job done. After you do that, going back to playing without restrictions will feel amazing!