First of all you are extremely squishy, so be on your guard and even tho this guide is designed for Middle lane it works very well on Bottom lane.

Buy your ring, followed by basic boots when you get the funds. This will be substantial enough for you do deal good damage for the first 8 levels. Your next item is going to be a blasting wand or extremely large rod. You want the Deathcap as fast as possible, its going to be big damage out the gate.

After your death cap get Cooldown Reduction boots. A lot of AP will choose the magic pen, however, Tibbers is your big bad body guard, and the more you can bring him out the better. It will bring your Tibbers cool down to just around a minute, and that is exactly what you need for annie.
You will be able to get stuns quickly and use Tibbers to burst damage squishy targets or crowd controll enemy teams.

With the first 4 big items to build + starter ring, you should be doing big hits. Morellonomicon and C/D boots should make you and Tibbers a powerful force.

Hourglass, Torment, and Lich Bane can all be substituted or picked in a different order. But Annie should be like a train coming through the house at this point.

Have Fun :) use Tibbers as much as you can! Hes an animal!