Out of all the epics your companions are offered, double tap 3 and burst fire 3 are 2 of the worst.
First lets start with what they do: Burst fire 3: bonus damage against wounded enemies Double tap 3: doesn't trigger quick draw
I think a good way to improve Burst fire/Relentless/Mojo Echo 3 is to make the chance to trigger it increase from 35 to 50 to 65 with each hit. I know you can improve the chance by using SAW buffs but still.
A good way to improve Double Tap/Blade Storm/Mojo Rising 3 is to have it increase critical chance by 2-3% each double tap hit, if it seems too little, make it 5% but I think that's too much.