Herein, how do you get the Horde Slayer title?
When you get a bounty on your head - the enemy faction see your location on the map, and you can't fly. Getting the bounty on your head also starts the quest The Horde Slayer. If you get 10 more kills while you have a bounty on your head - you get the quest and title.
Similarly, is the Horde Slayer title account wide? The Achievement appears to be account wide, I.e. you will get The Alliance Slayer when you unlock this on your Horde Characters, However the title will only be available on the character which you unlocked the achievement on.
Keeping this in consideration, how do you get the bloodthirsty title?
This is obtained by getting 250,000 honorable kills. Your honorable kills can be seen on the statistics tab under kills in the achievement window.
How do I get Alliance Slayer?
To get this you need honourable kills of 10 Alliance players while having a bounty on your head. This is obtainable before level 120 as I received it on my level 115 Feral Druid. Note while having the bounty, you can not die, disconnect or Log off.