It's very easy to solo Sha of Anger, and any level 100+ character should be able to do it without any problems. You can only get loot once per week, but the bonus loot has a chance to award the mount as well, so make sure to use it.
The loot is on character-basis, so you can easily farm it on your alts for extra chances at the mount.
The spawn time is currently 15 minutes, so it's not that long of a wait. When he spawns, he will yell across all the zone, so it's easy to see that he is up.