It seems slightly unusual to apply a binary checksum to an ascii message but I will assume it works as you describe it.
I suggest you use 'C' strings rather than the String class. Mainly because the String class exposes you to a memory leak which may render your sketch unreliable, but also because 'C' strings make it easy to access the individual characters (bytes) that make up the string.
'C' strings are essentially char arrays with a null character at the end of the content. Various standard library functions that operate on 'C' strings use the null terminator to determine where the string ends.
You need to compose your message into a char array and then process each element in the array to derive the checksum. It sounds as if a simple for loop and '^' (bitwise XOR) operator should do this. After appending the checksum to the message, make sure it is null terminated before any printing.