The only times we needed to get a bus was in and out of the rail station on a simple bus journey as it was a bit far to walk with a rucsac. Otherwise, central Edinburgh is remarkably compact to visit on foot with no need for buses. Also try a walk along the river Leith to the old port of Leith and then catch a 35 bus all the walk back - so simple! Modern art gallery is incredible for Surrealist paintings - and free, with a great cafe too.