When writing notes one does not use full sentences, only the necessary words. One way of saying this is we write in bullets. For example:
* no sentences
* necessary words only
Speaking in bullets means you use few words that come out suddenly, like bullets from a gun.
I can understand why. I agree with tepatria on the meaning and I think the choice of "shoot out" is unfortunate when used with "bullet" in this way. Perhaps it is intended as a pun on "bullet", but an unwise one I think.
Bullet is the typographical term used to describe the blobs which mark "bullet points", which is of course why they are so called: