With a process that's much more technical than you probably thought.
For this, you need to work with the Pokemon damage formula, the equation that determines the amount of damage dealt, which is as follows:
So the first thing you need to understand based on this equation is that Technician and STAB DON'T affect the value of the base power. Very common misconception. This means that, if you want to use the correct formula, multiplying all the boosts together like you did doesn't work.
You could, however, create a hypothetical base power by multiplying the value of "base" (which is 40 for Bullet Punch) by all the numbers in "Modifier". The results of this are very similar to when you'd use the actual formula.
Ignoring critical hits, rolls and Bullet Punch's effectiveness (for now), you'd get a formula that looks like this;
Base power = base (40) x STAB (1.5) x Technician (1.5)
So our base power for Bullet Punch, using STAB and Technician, is 90. Let's look at a calc showing how much damage this does to a Pokemon (using blank sets for simplicity):
0 Atk Scizor Bullet Punch vs. 0 HP / 0 Def Abomasnow: 206-244 (64.1 - 76%) -- guaranteed 2HKO
Now, the calc for the same Abomasnow except using the normal damage formula:
0 Atk Technician Scizor Bullet Punch vs. 0 HP / 0 Def Abomasnow: 206-246 (64.1 - 76.6%) -- guaranteed 2HKO
Only 2 HP difference! So they do basically the exact same thing. Just keep it mind that while multiplying base power by STAB and Technician gives basically the same result, it's not the right way to determine damage.
TL;DR: You don't change the value of the base power, but if you did, you'd basically get the same result damage-wise. The base power would be 90.