One can imagine a market for this developing on routes between major worlds. Picture a pool of loitering ships, each kept ready to jump on a moment's notice. Businesses wanting to get data to another world *right now* can bid for exclusive message transport. Ships that accept a bid then get the data beamed aboard (encrypted, naturally) with instructions where to send it in the target system. If a lot of traffic like this is happening, the market would probably be automated to connect businesses and ships quickly. And of course the really big players would have their own private messenger fleets, turning to the market only when they run out of their own ships, and perhaps putting excess ships temporarily on the market as well.
Again, this would only happen between pairs of high-traffic, big-business worlds. In the backwaters, you'd still get the PC-friendly scenario of the frantic businessbeing running into the starport bar waving a wad of credits and asking who can jump a message to Hellengonne XIV *right now*. :)