The first thing I would recommend is to take measurements. Where are you losing your time? Is it in the read, or the write?
Over 100,000 accesses (sum the times): How much time is spent allocating the buffer array? How much time is spent opening the file for read (is it the same file every time?) How much time is spent in read and write operations?
If you aren't doing any type of transformation on the file, do you need a BinaryWriter, or can you use a filestream for writes? (try it, do you get identical output? does it save time?)