How is a bit field represented in Quantum Computing?

You can represent the "A" as a series of qubits in the $vert 01000001rangle$-state. Any other representation would work as well, as long as there is consensus on the notation.

Regarding usefulness, most envisioned applications of quantum computers are as subpart of classical algorithms, where computationally hard problems are solved. Hence, 'typing' an "A" might not be necessary, though the development of quantum computers might prove otherwise.

Classical information is stored the same way as it is for classical computers. You cannot use quantum states to store (in a retrievable way) more information that you would with classical bits.