1) A more aggressive version of the word 'bye'; used to communicate a flexible variety of phrases to anyone of annoyance, as well as virtually any person who rubs you the wrong way; such as: "get the fuck out of here" or "bitch, get out of my sight NOW, before I hit your ass."
2) Accentuation of the "eeeeee" sound (i.e. BEEEEEEEEII) adds a more playful meaning to the word. Usually used to emphasize sarcastic humor when talking amongst friends.
3) Shorter forms of the word, when strong emphasis is placed on the "eei" sound, are used to give more intensity to the original definition (#1). Typically, this is used as an abrubt, simple ending to a conversation, argument, etc; sending the message of being fed up or 'done with the conversation'.
Definition 1 Scenario:
-You're arguing with a friend about something. You know without a doubt they are wrong and you are right. During the argument, your friend attempts to make a point that is clearly absurd.
>>Saying "Bei" can be used a quick response to insinuate that what was just said was wrong or ridiculous in some way.
Definition 2 Scenario:
-The woman on the phone in front of you at the check out counter looks a fucking fool. Her muffin top is hanging over her jeans (clearly too tight for pleasure), her dark roots are showing through her obviously amature-bleaching job, and she's wearing a Nickleback T-shirt (also ridiculously too small for her). You then look down to see that the bitch is buying nothing but Little Debbie cakes. You then hear her say, "Yeah, I know gurh. I need to be gettin to the gym. I'm about to start this new diet..."-
>>PERFECT opportunity. Turning to your friend, or whomever you may be with, you say something along the lines of: "Do you SEE this bitch? She looks like she's on a diet. BEEEEEEI!"-
Definition 3 Scenario:
-You are in a heated argument with someone who is being too bullheaded and ignorant for your tastes. It is apparent the argument is going nowhere and will accomplish nothing. You're now at the end of your rope.
>>Keep it classy. A sharp, "BEEIII" can be thrown in at any time to halt the discussion. Walking away, or ignoring the other person solidifies your message of being completely finished & over it.