There isn't exactly one short Buddhist bible (see Why isn't there a Buddhist Bible?).
The Tripitaka is the Pali canon, possibly the earliest (or at least, among the earliest) of the surviving Buddhist literature. It has three parts, and of these three the Sutta Pitaka is the most relevant (to us).
You can read it (or at least begin to read it) online. Web sites with the Pali suttas translated include:
- http://www.accesstoinsight.org/ -- popular, accessible, maybe a minimum of commentary
- http://dharmafarer.org/ -- suttas are introduced with a lot of commentary by the translator
- http://www.buddha-vacana.org/ -- not so many of the suttas are translated, but those which are here are given with word-by-word Pali-to-English translations
- https://suttacentral.net/ (click on "Sutta" in the heading of the page) -- perhaps the most extensive collection (for example if eventually you're looking for a specific sutta, and find that it's not one of the suttas translated on Access to Insight, then look for it here)
See also the answers to these topics:
Note that although the Pali canon (which is the associated with the Theravada tradition) is among the oldest literature, there are also newer (or later) Buddhist schools with their own canonical literature -- so if you want to find "all the teachings of Buddhism" you might also investigate Mahayana literature (including Chinese, Japanese, and Tibetan) as well as modern/contemporary literature.
The simplest answer to "how to behave, rules" might be to say "the five precepts".
I also liked, The Buddha's Teachings on Prosperity: At Home, At Work, in the World because it selects from the Pali canon the suttas which contain behaviour recommendations for lay-people. For example this answer is my summary of one its chapters (the book references specific suttas, which my summary doesn't).
Buddhism seems to me to be rather a large topic, so almost any introduction to it will give a somewhat distorted or one-sided view of it. In my answer to the topic New to Buddhism I tried to give an overview, and also said that people recommend In the Buddha’s Words by Bhikkhu Bodhi.
Another answer wrote that "Buddhism is not a religion based on a Holy Book" which is more or less true:
- If you are one of the so-called People of the Book, perhaps you could over-estimate the importance of a "book" or Bible.
- Even so, some words that I guess may be equally important in Buddhism include Buddhavacana, Sangha, Dhamma, (not to mention "lineage"), and various (practical) practices.
So instead of or as well as a Bible, people might recommend you look for (one or more) Buddhist teachers and/or communities.