No you cannot write less than a byte. A byte is an indivisble amount of memory the computer can handle. The hardware is not equipped to handle units of data <1 byte (though the size of a byte may differ from machine to machine). The file system also deals with data in units of blocks which may be 4KB, so writing one bit really results in a 4KB block on disk.
See also the more general version of this question: It is possible to write less than 1 byte to a file