a few hours .. i would dedicate 4 hours (but it will probably take more like 3, including travel time)

yes there is. if I remember correct it is Bus #25 but double check. Salzburg is covered in a great public transportation network. Get a 24 hour pass in advance. you can get them at a Tabak Traffik (small store that sells cigarettes, prepaid phone cards, etc). The use of the ticket starts when you validate it inside the bus on a machine and is valid for 24 hours from that point. You can also get the 'Salzburg Card' which includes entrance to attractions as well as the bus system.