That's what the compressed gas is - it's potential energy. It's like a battery.
> Like how I can't fill my car tire with my bike pump.
Why not? Because you can't pump hard enough and it's not strong enough to hold the pressure needed? You can build a stronger pump, and you can use a lever or gears (same thing really) to compensate for your strength if you can't pump any more.
> Presumably you could fill the tire of a transport truck with the bulb from a blood pressure cuff and a lot of time, but it's not intuitive to me what the mechanics are in between those two things.
Again that's just a 'lever' problem - you can't squeeze the bulb hard enough, so add a lever (and you may need to make the bulb stronger.)