In the Power Armour History it says "While wearing this armour, the wearer never suffers any penalties for moving and firing with a pistol- or basic-class weapon on semi- or fully automatic fire.", but you didn't suffer any penalty on semi-automatic fire, you don't get the +10 Bonus to BS.

Does this mean Bring Death from Afar also grants the +10 Bonus for semi- and the +20 Bonus for full-automatic fire while moving and firing?

If shooting with basic or pistol weapon on burst mode you get no bonus for the fact you're moving your AgB in meter, in full auto you get -10% BS for moving while shooting.

The +10% and +20% are avaible only when standing still and not moving (no more than the half of your AgB.

Therefore with the trait "Bring death from afar" you can both move your AGB in meter and also get the +10% from burst or +20% from full-auto.

Sorry forgot something and still no way of editing the message.

Bring death from afar make Heavy weapon stand as basic weapon so you can move and shoot with your heavy weapon and make it without penalities.