In Bohrs calculation for finding the radius of orbit of electron, we have used the concept of particle nature of electron (for quantization). But no information is available for the amplitude of such electron wave. what if the amplitude is greater than the actual radius of the orbit and the electron thus touches the nucleus?.
You aren't supposed to try to imagine the wave in Bohr's model. This model was a first attempt at creating a somehow-working model of a stable atom. Bohr's model is now superseded by quantum mechanics, which has much more sense in its definition of the wave function.
Quantum mechanical wave function doesn't represent a wave on a membrane around the nucleus or anything like that. It's more similar to electromagnetic wave: merely a function defined for all space and time. Square of absolute value of the amplitude of quantum-mechanical wave function defines probability of finding the electron in the given point as per Born rule.