Bloom is how far apart the crosshair on a gun will spread(bloom) while firing. Lower number = more accurate when firing many rounds at a time.
As for falloff damage, I'm not sure what the number represents, exactly. As you would think though, fall off damage is how much the damage 'falls off' after a certain range has been reached, until you do no damage and the shot disappears off into yonder sunset.
If someone knows what the number represents for fall off damage(ie, you will always do at least this much damage, or damage of weapon minus whatever the fall off number is, etc), and could clue me in, that would be wonderful as well.