The fastest way to gain Prayer experience depends on whether the player is a donator or not.
As a donator, it's recommended training Hunter first until level 83 to be able to catch dragon implings in the donator zone. After all, looting dragon implings yield a lot of (baby)dragon bones. Besides having the required Hunter level, players must wield a butterfly net and have an empty impling jar in their inventory to hunt dragon implings. Because of the fishing spots in the donator zone, hunting dragon implings can be easily combined with gaining Fishing experience at the same time.
Otherwise, it's advised to complete the medium achievement Dragon Hunter II by killing 350 dragons, as the reward for this achievement is 200 dragon bones, in addition to 250,000 coins. In order to complete this achievement, it is best to kill green dragons in the Wilderness or, in view of gaining Smithing experience later on, mithril dragons, because they drop noted mithril bars.
After the medium achievement, the hard achievement Expert Dragon Slayer can be completed by killing 950 dragons. This will yield the player 1,000 dragon bones along with 1,000,000 coins.
Killing Zulrah is also one of the best methods to obtain dragon bones, as it frequently drops 30 noted dragon bones.