There seems to be some confusion between speed and velocity - the latter being speed in a particular direction. To change velocity requires a force. If you apply a force to a mass it accelerates.
Thus, a turn changes the velocity (ie changes the direction) even at a constant speed. Where does the force come from to change the direction of an aeroplane? It comes from the lift of the wing. We bank the aircraft so that a part of the wing's lift acts to change our direction.
It's impossible to tell whether uniform air is moving or not without reference to something. When airliners travel in the jetstream, their groundspeed can be pretty high, but whatever measuring device you attached to the airframe it would still record the speed of the aircraft through the air. So in uniform air, if you put up the screens and focus on the instruments you will be unable to tell whether the air mass around your aeroplane is moving relative to something else or not. You'll simply execute the turn and it will be completely undramatic. Try it some time (we all have!) at altitude - it's a total non-event.
So what happens closer to the ground? Well, there are a couple of factors.
- Close to the ground the wind tends not to be uniform. Friction slows down air nearer the surface and turbulence arises from obstacles. Each of these in their own way mean that the aircraft is no longer in a uniform block of air. We typically compensate for these (and gusting wind) by slightly increasing our airspeed so that our angle of attack at any point across the wing remains lower than the stall angle.
- At low levels we often have (as GA pilots) constraints of circuit shape, ground features to avoid, runway to aim at etc etc. Our flying is consequently done with reference to the earth and not to the air mass (ie we take our eye off the ASI). The change in reference is dangerous and I suspect it's that which ultimately leads to stall/spin.
Keep safe.