I've been in Edinburgh once before: in 1984 I was traveling with a friend on an Interrail pass for four weeks all through England, Wales and Scotland. For two nights we stayed in Edinburgh. But the only thing I remember from that trip was the youth hostel we stayed in.
The camping site I'm staying at is at the outskirts of the city. I consider using the bike to get to the center, but I don't want to leave it unattended in the middle of a big city. There is a bus stop directly outside the camping site. The fare is £1.10 for single ticket to anywhere in Edinburgh, or £2.50 for a day ticket. I buy a day ticket and board the red double decker bus.