The Edinburgh Bus Tours confusingly but generously offers three different tours and buses: City Sightseeing Edinburgh, Edinburgh Tour, and Majestic Tour. We bought the Royal Edinburgh Ticket and rode the green bus (the only one with a live narrator).
You can ride ANY of the three different tours for the one company. That ticket gave us Edinburgh Castle admission, Holyroodhouse Palace admission, AND the HMY Britannia admission, a fabulous bargain. When you buy your ticket at the Waterloo stop, you have to specify the timed entry for the Castle. We didn't need timed entries for the Palace or yacht. Tip: getting to the Waterloo stop could involve a climb up Jacob's Ladder, despite Google Maps saying the walk is "mostly flat." Mostly, except for about 100 steep stone steps!
The bus ticket is hop-on, hop-off for 48 hours. Even after the bus ticket expires, you STILL can use the admission tickets! We squeezed in a trip out to the yacht (Britannia) using a cab, so the ride was pricey but the yacht tour was great.
The bus tour is detailed and a great mix of history, personalities, intrigue, and modernity. Architecture, politicians, Burke & Hare, Deacon Brodie, the Honours of Scotland, the castle's defenses, and the Harry Potter book series are all included in the narration. Bus stops are well marked and getting on and off is very easy. The driver is very patient so you don't have to rush.
All three attractions are great to see, even if you think you won't like them!