Disclaimer: I'm a Physicist, not a historian.

The problem with your assertion is that the Bernoulli principle is not the only thing required for powered flight, far from it in fact. As the term implies, you need a power source. Steam engines of the type that were coming into prominence at the time of Bernoulli's discovery were hardly lightweight and portable, indeed steam engines as a whole are unsuitable for use in an airplane as they require a large amount of space for the steam, condenser, turbine and heating apparatus.

Internal combustion engines (the type used in most vehicles nowadays) only came about in the early 19th century, however even then it took pretty much a century for them to be developed to the point where the power to weight ratio was sufficient for powered flight.

Next you have to consider the control mechanisms for the aircraft, which have a not inconsequential amount of complexity and required some trial and error to get right; the earliest theoretical designs appeared in the mid 19th century, however they were refined over time through testing on glider designs.

When you factor in the time taken for all the prerequisite technologies to be invented and developed enough to be feasible, it becomes more apparent why powered flight doesn't appear until the Wright brothers - the engine, aviation theory, manufacturing techniques and other technical knowledge was just not there during Bernoulli's time.