As far as I know there is no standard tool capable of doing this. Yet I can think of several ways of achieving this, each with their drawbacks.
If you know which process will access the file/directory and you are sure this process does only few or no other I/O you can parse
/proc/PID/io and determine the amount of read/written bytes by looking at
wchar (any I/O) or
write_bytes (disk I/O) or even
syscw (number of read()/write()-like system calls).
If you don't know which process will access the file/directory (but you are sure these processes do only few or no other I/O) you have to watch the location using the
inotify feature, determine the PIDs and then do the mechanism described in the previous paragraph.
If the process determined does other I/O it gets a little bit more complicated. You have to
strace it and sum up the offsets of all read/write calls of all file descriptors pointing to your file/directory.
All of these solutions aren't accurate to a single byte but can give you a good estimate.