How does the bypass air provide thrust?
The bypass air is accelerated by the fan at the front of the turbofan engine. This changes its velocity and therefore its momentum, which is the definition of a force (in this case: thrust):

$$ F = \frac{\text{d}}{\text{d}t} p = m \frac{\text{d}}{\text{d}t} v = m \cdot a $$

This thrust contributes to the total thrust of the engine. How much will depend on the bypass ratio of the engine and other parameters, but 80% is plausible for a high bypass turbofan. Bernoulli's principle has nothing to do with this.

You can see the accelerated airflow in the following animation:


(source: Wikimedia)

The air coming from the engine core will move even faster, but there is less of it in a high bypass turbofan resulting in less total thrust coming from the core:


  The fan airflow, referred to as the cold air stream, is accelerated by the fan and passes through the engine remaining outside of the engine core. The cold air stream moves much slower than the hot stream gas flow passing through the engine core.


(skybrary.aero)