Danny Thompson of PENTANGLE fame has already been mentioned, but he does a lot more than just PENTANGLE. [ 'Reflections' is a great example of their jazzier more prog influenced work ].
More recently he's worked with Jakko Jakszyk on some tracks on Jakkos solo, ' The Bruised Romantic Glee Club' and earlier in the Indian influenced ' Dizrhythmia'. Even earlier, Danny's solos , particularly ' Whatever ' is very good in a jazz/folk/proggy kind of way and well worth a listen.
But in the more fusion mould, Christian McBride from the US is a monster of the double bass. He has a number of interesting releases. A good place to start with him, particularly if you like STING's jazzier incarnations ,is the great Sting DVD ' All This Time ' , where despite Stings use of his old Fender bass, Christian powers along with Manu Katche on drums in what is a sublime band.
Said band is largely acoustic [ hence the appropriate input from Christian ] and Sting rearranged some of his old classics in a really interesting Jazz oriented way . [ You've just got to love the souped up version of ' Roxanne' featuring Jason Robello on grand piano as well as an unforgettable version of ' An Englishman in New York ' which is given similar treatment.] Suck it and see.