How much will a hole in the wing of a bumblebee affect its flying?

While a full fluid dynamic and biomechanical treatment is complex, I think one can make a simple scaling argument:

Bumblebees are small. That means that the Reynolds number of fluid flow around them also gets scaled down; in fact, to a bumblebee air is a pretty viscous fluid. Hence the resistance to flowing through a small hole will be pretty big.

One can roughly estimate this by thinking of the hole as an orfice plate (in a very large pipe, so $\beta\approx 0$). Since the mass flow is proportional to the surface area of the hole we should guesstimate that a 1% hole has a pretty minor effect both on escaping air and the overall flow pattern.

In fact, looking at small moths one often finds that they have wings that are little more than a few feathers with pretty noticeable holes. This is just like how one can use a pole not just to push a punt in a river but also use it as both an oar and a rudder: in the viscous water environment the rod has enough area to matter anyway.