Tim is right,

Burst Fire should add an extra bullet to doubleshot for a max of (3) from Burst Fire Skill Level = 1
From there it's Damage scales through to Level 20

Thanks CosairTim, you found a real one. Burst Fire is one of three Pre-BB "upgrade" skills (with Wrath of the Octopi and Bullseye): it was never meant to sit on a key of its own, so not being able to drag it is how the original game works. What was broken is the other half: a point in Burst Fire should turn your Double Shot key into Burst Fire, and it did not. That is fixed: with at least one point in Burst Fire, Double Shot fires three bullets with Burst Fire's own damage and MP cost. The same now applies to Octopus -> Wrath of the Octopi and Homing Beacon -> Bullseye. Please re-test on your Outlaw.