Would biplanes be of use in VSTOL applications? What is the down side to biplanes? ex. Bush Pilots or VSTOL competitions
You're quite right in not doubting the capabilities of biplanes, like Curtiss Pitts with the fully aerobatic Pitts Special.



Aerodynamically, the classic biplane has many disadvantages, with drag being built in everywhere. Like designing an aircraft with a built-in airbrake that is deployed all the time. The double wing creates more drag than a single wing, the struts create extra drag, and the cross-wires between the wings are easy to miss on photo's but are huge contributors to drag as well.

Structurally though, a biplane design is quite advantageous. The biplane configuration acts like a box design, much easier to integrate with the fuselage than the cantilever clean wing with its bending moment at the wing root. So if the construction is exposed to high acceleration like a fully aerobatic plane, there is less aeronautical engineering involved. As usual in aeronautics, aerodynamic disadvantages equate to structural advantages.

But zooming out even further, it makes little sense to create lift together with a lot of drag. Aerodynamics determines the stall speed of an aircraft, the biplane has no advantages here. If the objective of the bush pilot is to fly slowly and inspect, and to have VSTOL capabilities, there is a much better option available: the autogyro. The owner of Quobba Station in Western Australia has built one himself and uses it for inspecting his huge property. They are used as airborne motorcycles for sheep mustering etc. Upon engine failure (which has happened), it can be landed safely anywhere on the property. Just bring a hat.



Update

The thought that biplanes must have slower stall speeds than comparable monoplanes keeps nagging me, but I cannot find an explanation or indication that that is actually the case. For instance for the Tiger Moth: Stall Speed = 40 KIAS @ 827 kg. For the Cessna 172: Stall Speed = 40 KIAS @ 1145 kg. 

A biplane could be designed for lower stall speeds and good climb performance: make the wing area much larger than required, with an associated lower wing loading. But this can be done in a monoplane as well:


Simply use a large single wing.
Increase wing area in landing/low speed configuration by using Fowler flaps.
Increase wing camber in landing configuration.


And then it becomes a matter of economics, is it cheaper to build a biplane than it is to build a monoplane with fancy flapping arrangements? Probably. But all the dragginess will cause much higher fuel consumption, and it will take a long time before the pilots get to where they want to be.