You can still use the method accepting a string to send bytes because that uses ASCII encoding by default (converts each character to an ASCII byte value).
So the binary value 0x01 can be send as
serialPort1.Write("\u0001");
But if you need to send data containing a null byte, values >= 128, or avoid the Unicode to ASCII conversion, you must use the method accepting a byte array:
var dataByte = new byte[] { 0x00 };
serialPort1.Write(dataByte, 0, 1);