Bias-variance tradeoff and the uncertainty principle
No, the uncertainty principle describes a property that is specific to electrons. That electrons don't display their wave and particle properties simultaneously. Here from Wikibooks:


  The Heisenberg uncertainty principle states that the exact position
  and momentum of an electron cannot be simultaneously determined. This
  is because electrons simply don't have a definite position, and
  direction of motion, at the same time!


.


  This is due to the fact that electrons cannot exhibit both their wave
  and particle properties at the same time when being observed to
  interact with their surroundings. The momentum of an electron is
  proportional to its velocity, but based on its wave properties; its
  position is based on its particle position in space.


The bias-variance tradeoff describes a property of predictive models. That error from bias and variance usually exist in a tug-o-war where you cannot decrease one without increasing the other and that you have to find the perfect middle ground. You can observe it here from this Medium:



I agree that there are some similarities. There is a sort of tradeoff between measuring the momentum and position of electrons. But they are not the same thing.