Can a very high concentration of hydrogen peroxide, inhibit or denature the enzyme catalase?
20% hydrogen peroxide sounds HUGE. But something can happen that is called substrate inhibition. It can be detected if the substrate acts as a non-competitive reversible inhibitor (i.e. binds only to the active ES Michaelis complex). In the case I studied during my PhD, the inhibition constant ($K_\mathrm{i}$) was roughly 1000 times higher that the Michaelis constant ($K_\mathrm{M}$). 
The steady-state rate was well fit with :
$$r = \frac{r_\infty}{1+\frac{K_\mathrm{M}}{s} + \frac{s}{K_\mathrm{i}}}$$
So the activity would go through a maximum ($s$ is substrate concentration).

Tip : if it is possible, do you assays with substrate concentrations growing exponentially, like $1\,\mathrm{\mu M}$, then 2, 5, 10, 20, etc.

A good way to decide between enzyme denaturation and substrate inhibition would be to know if it is reversible : denaturation must not be reversible. You could first make a baseline assay (at low conc.), expose the enzyme to a high concentration, then change the composition of the solution (eg dialysis, dilution) and run another assay at low concentration.

A "volume of bubbles" does not sound very accurate. Could you use a Clark electrode to measure the activity instead ?