The Origin

"Good thing I'm on my bee" (sometimes just "I'm on my bee") is an exploitable image macro originating from 4chan's /b/.
In the original post, a user said that "The floor is now lava", and others began thinking up ways of avoiding it- one user claimed that "He was safe on his bee" (Misspelling of "bed")
Others began mocking him, and one user created an image macro of a young boy riding a bee, safely avoiding lava.

What it Means

Within the context of the meme, it is understood that being on one's bee is a mark of safety, preparedness, status, bravery, or just luck. The best examples of "I'm on my bee" depict our brave hero on his bee, fleeing some kind of famous disaster or dangerous situation.