(12 Aug 2015, 4:07 pm)BusLoverMum wrote Just googled
bus edinburgh waverly to annandale street
and got a couple of suggestions - namely the 25 from princes street to craigentinny or the 49 from leith street (walk) to magdalene.
http://lothianbuses.com/assets/files/r25_130324.pdf
http://lothianbuses.com/assets/files/r49_130324.pdf
It's probably no more than a ten minute walk from Princes Street, but there are loads of buses which stop within a few minutes walk.