The recommended and most fun way to learn about Bullet is to use the Example Browser. It is part of the Bullet SDK.

The Bullet user manual and related documentation are in the docs folder of the Physics SDK:
There is also online API documentation.
You can re-generate the API documentation by running Doxygen in the root of Bullet

The PyBullet Quickstart Guide shows how to use PyBullet, which is useful for Robotics, Virtual Reality and Reinforcement Learning. Some OpenAI Gym compatible environments are provided, with TensorFlow pre-trained models.

If you want to learn more about the algorithms of Bullet, here are some slide decks from a SIGGRAPH 2015 course:

Introduction to rigid body pipeline, collision detection

Advances in constraint solving, Featherstone Articulated Body Algorithm

Acceleration of the full collision detection and constraint solver on GPU

For further information, questions and feedback please use the forums.