To understand this phenomenon we need to look (rather more) carefully at what Bernouli actually means and how we apply it.
Bernouli said that the total pressure (dynamic + static) in an airstream is constant. In doing so he made a number of simplfying assumptions including the conditions that no energy would be added to nor subtracted from the airstream. The basic logic of his argument is that if no energy enters or leaves teh airstream, then the energy within it remains constant.
The energy posessed by the air is evident in various forms. The most signifcant of these are its temperature (heat energy), static pressure (mechanical energy) and dynamic pressure (kinetic energy). Kinetic energy and hence dynamic pressure are proportional to TAS squared. So if the TAS increases, the dynamic pressure increases. But for the total energy to remain constant, this increase in dynamic pressure must be acompanied (funded by) a corresponding decrease in both temperature and static pressure. So if the TAS of the airstream increases, the staic pressure decreases. This might lead us to (incorrectly) conclude that static pressure will decrease as an aircarft accelerates.
To understand why this is not the case, we must remember that all of the above argument is based upon changes in the absolute (or real) TAS of the airstream. In the case of an aircraft, it is the aircraft rather than the air that is moving. Although it is convenient to use the aircraft as the reference point and visualise the air as flowing past it, this can be misleading.
Consider an aircraft accelerating down the runway. Its TAS relative to the entire atmosphere is increasing. If we treat this as an increase in the TAS of the entire atmosphere, then the static pressure in the entire atmosphere must reduce. Worse still, with the very large number of objects moving through the air (including birds, bullets, cars, animals and suicidal stock brokers) the static pressure would be extremely low indeed. This argument is clearly not true.
It is more accurate to say that as the aircraft accelerates, the kinetic energy and dynamic pressure relative to the aircraft increase, but the static pressure of the general atmosphere is unaffected. This increased dynamic pressure and constant static pressure mean that the total pressure affecting the aircraft increases.
But when the air passes close to the aircraft it (the air) must accelerate in various directions to make room for the aircraft to pass through it. These are reall accelerations, representing changes in the aboslute velocity of the air. Because they are reall accelerations, they cause real changes in dynamic and static pressure. The camber of the wings, for example causes a real increase in the TAS of the air passing over them. This causes an increase in dynamic pressure and a decrease in static pressure. The overall effect being lift (and unfortuantely drag).
The real velocity or the air at all points on the surface of an aircraft will of course be affected to some degree. The trick in providing accurate measurement of static pressure for barometric instruments, is to find an area where the reall accelerations and hence changes in static pressure are the smallest.