This is really a rules question (should go in the You Make The Call forum, rather than Army Lists), but I'll answer it here.
The short answer is that the only way to get a Bloodthirster in a Beasts army is by playing 3000pts or more.
When you make a Chaos army, the type of General you have determines what kind of army it is (Beasts, Mortals, or Daemons). The General is always the character with the highest Leadership, unless he cannot be due to a special rule (I think Chaos Sorcerer rules say they can't be the General if there are any other characters, or something similar).
If you take a Bloodthirster he uses up a Lord slot, and since he has higher Ld than any non-Lord character, he must be the General. Unless you're playing 3000pts or more, which allows you to field two Lords, and you pick another Lord with equal or higher Ld.
If a Bloodthirster is your General, Beasts units are special, and Daemons are core. So you don't really have a "Beasts army", per se. At 2000pts you could take three minimum core Daemon units, then max out your Special and Rare units with Beasts stuff, which would give you what is technically a "Daemon army", but with lots of Beasts units.
The Daemonic Gift "Unliving Idol" allows a Daemonic General to have Beasts units as core. This is great for leading a Beasts army with a big Daemonic character. However, you're not allowed to choose additional Gifts for a Bloodthirster, so he can't take Unliving Idol. You CAN lead your Beasts army with a Daemon Prince or Exalted Daemon by giving them Unliving Idol.