Hmm. Interesting. I'll take a wild-ass guess too.

Turbulence is essentially inertia. That is, when an object's medium
changes, the object experiences acceleration or deceleration until the
medium and object are in balance again.

When the air mass changes, the airplane accelerates in some direction
(up, backwards, sideways, whatever) to match it. If the air mass is
constantly changing (unstable air), the airplane is constantly
adjusting (bumpy ride).

I wonder if the airspeed was reading higher because it actually was
higher, i.e. you entered an air mass which had an average higher speed
relative to the direction of the airplane.

I think this would apply to what would feel like an updraft. The
second most important thing that an airplane does is provide lift when
you give it airspeed. A sudden supply of airspeed would give a sudden
burst of lift, and feel like an updraft. In fact, I think that would
be a lot more efficient way to lift an airplane than blowing air up
from underneath it at any speed.

I'll throw this bit of empirical observation in too: If you take an
airspeed indicator out of an airplane, and hold it in your hands and
shake it, it will indicate changes in airspeed.