Confusion abounds in conversation relating to Bernoulli's principle, so I will do my best to dispel some of the more pernicious misconceptions.
(1) Bernoulli's principle, in general, applies only to a single streamline, with unique stagnation properties. While many aerodynamic/hydrodynamic flows (e.g. irrotational flows) do exhibit uniform stagnation pressure everywhere, this is generally not to be expected. Case in point, even though the static pressure just inside and just outside your car window are equal, the stagnation properties will be very different (higher outside, substantially lower within the confines of the car, where the flow is a swirling welter of separated flow). Faster velocity does not always mean lower pressure, contrary to what many are led to believe. You must look at the flow as a whole, especially the upstream conditions.
(2) Stagnation properties do in fact depend on the reference frame, while static properties do not. That is to say, stagnation properties are relative. In the stationary (ground) reference frame the ambient air is not moving, so the static and stagnation properties are identical. However, in the car's reference frame, the flow far upstream is moving rather quickly, so it's stagnation pressure, temperature, and density will necessarily be higher than the corresponding static values.
(3) Pressures, or more accurately, pressure gradients cause accelerations in an ideal flow, not the other way around; forces cause accelerations, not vice versa. This is a big source of confusion when talking about aerodynamic lift, vorticity distributions, and the Biot-Savart Law, but just keep in mind the difference between a physical principle and a merely useful mathematical tool/concept. The phenomena are coupled via conservation of mass and conservation of linear momentum, but ultimately the imposed pressure field causes the observed velocity distribution.
(4) It's best not to construe Bernoulli's principle as an expression of conservation of energy, as technically it's not (it completely neglects internal energy). No, Bernoulli's principle is best understood as an integrated expression of the conservation of linear momentum, $F=ma$, where nominal force is replaced with force per unit volume (which is equal to the negative local pressure gradient), and mass is replaced by mass per unit volume (which is the fluid density). In these terms, Newton's Second Law becomes:
$\frac{Force}{Unit Volume}=\left(\frac{Mass}{Unit Volume}\right)(Acceleration)$
which gives us
$-\frac{dP}{ds}=\rho v\frac{dv}{ds}$
which is rearranged as
$\frac{dP}{ds}+\rho v\frac{dv}{ds}=0$,
or
$\frac{dP}{\rho}+vdv=0$,
which when integrated gives us the classic incompressible Bernoulli Eqn.:
$\boxed{P+\frac{1}{2}\rho v^2=P_0}$,
The best reference on this topic (like most topics concerning fluid mechanics) is the NCFMF series entry entitled "Pressure Fields and Fluid Acceleration," hosted by the legend himself, Ascher H. Shapiro. He clears up a lot of the confusion surrounding this concept in a readily intelligible and fascinating way.
https://www.youtube.com/watch?v=8VrTpLa4qbM
Best Answer
Bernoulli's equation is frame-dependent as the following paper shows it in a nice way
The Bernoulli equation in a moving reference frame
The essence of the argument is to realize that in a frame where the obstacles, around which the fluid moves, are not stationary, these surfaces do non-zero work. And one must account for this work done when using the Bernoulli equation.
A better way is to look at the generalized Bernoulli equation as done here, which also covers viscous fluids.