With this code:

SERIAL: CLR TI
MOV A, #'A'
MOV SBUF, A
JNB TI, SERIAL
SJMP SERIAL

you are never waiting for the byte to be sent before writing the next byte. Lets look at what happens. TI is intially cleared. Then you write a char to SBUF. TI will be set only after the char is transmitted. But your jmp say if TI is not set go back to "serial" where you clr TI and write a new char. You need to wait unti TI is set before writing your next char to SBUF
Try this:

SERIAL: CLR TI
MOV A, #'A'
MOV SBUF, A
JNB TI, $
SJMP SERIAL

Bill