Princess was very cagey about whether was a shuttle bus. At the talk they said it was discontinued, but then on one of the pamphlets they said there was a shuttle, and the local person they brought onboard said there was indeed a shuttle. At the one talk they made it seem like you could either take train and walk 103 steps up or else book their overpriced excursion. Their "on your own" shuttle to Edinburg was $65 a person! But there was indeed a shuttle for a quite reasonable priced which I think everyone who intended to take the train took since they saw it was so easy to do.
The buses leave right from the pier and leave as they fill up. They leave every half hour from 1-5 out of Edinburgh back to ship. very efficient.
I would also warn people the tenders take a long time in Edinburgh. We were down there at time of docking at 8AM and were like number 300 for the tender. People who got there 8:30 were like 600 for tender. We had to wait 45 minutes for tender and tender takes 15 minutes. So we were not out till like 10 o'clock. I would recommend to plan accordingly in Edinburgh or else get down the dining room at like 7:30 or before to get off the ship. Even then, they did not start letting people off till 8:30 since they were a little disorganized with the tender.