John Patitucci demonstates some different bossa nova bass lines in this video.  He also breaks down a bit of the music theory involved when playing bossa nova bass rhythm. This is just a sample of the hundreds of videos in his jazz bass lessons.

As he explains, the bossa nova tempo is typically medium paced, to speed it up too much would turn it into a full on samba (which Patitucci also covers in his jazz bass lessons).  So, it's primarily a half note rhythm with a few dotted quarter eighth notes thrown in for good measure.

You want to settle into the rhythm of the drums.  Your job on bass here is to anchor the music, to bring out the rhythm of the other instruments.  Be sure to keep it relaxed though, bossa nova has a very laid back, mellow vibe to it. 

Be sure to be listening to other instruments as you play along here and have some fun with it.  Always remember to be incorporting feeling and emotion into your playing (read more about playing with expression here) - those are the non musical elements which will really bring out the music. 

Related Jazz Bass Blogs:

• Right Hand Playing
• Playing with Expression
• Jazz Bass Mastery with John Patitucci
• Jazz Bass Tip: Diminished Triad
• Two Beat Feel with Jazz Triplets