Itu hits the nail on the head. The ADSR of a sax (the way the note starts, continues and fades away) is controlled throughout by the breath. The strings of your bass have an initial 'pluck' then gradually (or quickly) fade away.
Basically you can control the way the note is played throughout it's duration on a saxophone, but without something like an ebow, all you can do on bass is pluck it.
There's all sorts of possible solutions available with an ebow, eq, volume pedal. To be honest I think a bari sounds best when it's HONKED staccato. Flats and foam is probably the simplest way to get a similar tone.