I've written & played bass parts on synths as well as bass guitars for ages & really enjoy it.
I personally think that for anything below a bottom E a synth sounds better, even though I've got a pretty nice 5 string bass.
I've never heard any kind of synth add-on for a bass guitar that sounds anywhere near as good as a decent keyboard synth does.
Used lots of stuff over the years - Moog Prodigy (awesome!), Sequential Circuits Pro One, Roland JP800 & Currently using a Korg Triton LE for all my keyboard stuff.