There's a couple of options available. You could fit a midi pickup (Roland do one) & that plugs into a converter which you could then plug into any midi synth.
There's synth access instruments from the likes of Godin (works on the same principle as the above.
There's midi guitar controllers that look like a bass, but have rows of buttons instead of strings & frets.
Or you can buy a few fx pedals & route them to make your bass sound like a synth.
Quite a few of us on here do the latter, as it allows you to build something that has your own sound.
Basic pedals for getting there are dirt & filter. Octaver on a wet setting also helps get more synth sounding & then you can get carried away.
Shep (Pantherairsoft) has a good blog for explaining how to use effects.
Jarman Donohue from Men Imitating Machines uses a full midi setup, Shep did an interview with him on his blog.
He can be found on Organic Bass Wobble Facebook page if you have any Qs about his set up (he's a helpful & friendly chap).