***** NOT A TEACHER *****
I believe that many books would recommend a comma after the word "bullet."
As I understand it, it is a shorter way to say something like:
"He shot the bullet, an act that killed many people inside the room."
Regarding the grammar, here is what a great grammarian has to say:
"A full so that clause of pure result ... can be abridged to a participial clause."
The scholar then gives this example:
1. He mistook me for a friend, so that he caused me some embarrassment.
2. He mistook me for a friend, causing me some embarrassment.
3. He mistook me for a friend, thus causing me some embarrassment.
Source: Page 293 of volume II of Professor Dr. George Oliver Curme's magisterial A Grammar of the English Language (1931).
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