Well, the obvious path would be south from Dale to the Old Dwarf Road which traversed Mirkwood; crossing the Anduin south of the Carrock; following the High Pass over the Misty Mountains, and then following the East-West road through Eriador to Hobbiton. For a large party (which I imagine was the case with those escorting Bilbo's packages), I doubt there would have been much trouble, especially since Grimbeorn's folk had done much to secure the area between the High Pass and Western Mirkwood.