The Bronze Drake is probably the easiest Drake to acquire in World of Warcraft at the moment. At level 90 any class with any type of gear can get it in 20 minutes easily.
To get the Reins of the Bronze Drake you will need to complete the Culling of Stratholme instance up to the Infinite Corruptor in 25 minutes. This shouldn’t ever be a problem at level 90 and you can probably do it with 15 minutes to spare most of the time.
So head over to Tanaris and into the Caverns of Time and then enter The Culling of Stratholme. Like the other Caverns of Time instances this instance is heavily story driven. Talk to the little gnome a bit into the instance when you enter. Follow the instructions. The crates you are looking for are all outside houses on the path to Statholme, use the item you got from the gnome on the 5 crates then meet the gnome outside Stratholme. Watch Arthas talk for a bit then move inside Stratholme. If nothing is happening at some point you will probably have to talk to Arthas. Now kill the 10 waves of mobs, move around to find them all, a new wave will spawn somewhere in this area when you have killed a wave. When you have killed the waves of mobs, meet up with Arthas outside the Town Halls. Now just follow Arthas and kill mobs. At some point Arthas will stop and tell you to talk to him when you are ready. Go straight ahead and then left and you will see the Infinite Corruptor. Kill it and loot the Reins of the Bronze Drake.