Jazz is all about the bass, Yo.
My recommendation for jazz bass is actually very simple on the technical side:
Make the "Soft Petals" sound in Reason (which is under "instruments" then under "Electric Piano") have higher Decay than usual (I do +20 on the middle nob that reads "Decay," not the rightmost nob that reads "Decay").
But it's trickier on the songwriting side, because you need intuition for it. It took me a long time to get this part of it down. Anyway, you'll need to have it play notes at unexpected times (while still often playing a note at the beginning of each measure), with the occasional really fast part that comes in as a surprise. Perhaps, a good first step would be trying to imitate the bass in Matchbox 20's If You're Gone - it's not super snazzy/jazzy/makeyouwanttogetupandshakethatgroovething bass, but I can see the jazz bass influence in it (that's what jazz bass + soft rock equals, IMHO).
Anyway, your stuff certainly shows potential. I know horns are one of the lacking sounds in Reason 4.0, so I understand how that's hard to do here. As a result, I haven't tried to make gentle horn sort of sounds with Reason 4.0; I've just tried to make triumphant horn sort of sounds. Do stick with it, for sure.