the title of your thread is wrong -- you want to remove the first byte from the string (not bits).
Code:
printf("%s\n", &mystring[1]);
or you could shift all bytes left
Code:
strcpy(mystring,&mystring[1]);
BTW: I've never found strncpy() a very useful function when copying null-terminated strings. strcpy does exactly the same thing that you posted, and has fewer parameters. Usually that third parameter is the size of the destination buffer, not the length of the source string, to avoid buffer overflows.