mov ax,ds
mov es,ax
mov si,my_string ;point it to my string
call PrintString

nop
hlt

my_string db 'h','i',0

PrintString: ;PrintString --es:si points to the string
mov ax,es
push ds ;I don't have segment overrides so..
mov ds,ax
;set it up for bios int 10h, ah=0Ah
mov ah,0x0A
mov bx,0
mov bp,0
print_loop:
mov al,[si+bp]
sub al,0 ;eventually replace with cmp
jz print_done ;if it is the end of a null terminated string then stop
mov cx,1
int 0x10
;temp only!
push ax  ;save ax
mov ax,bp ;we just add 1 to bp
add ax,1
mov bp,ax
pop ax
jmp print_loop ;do loop

print_done:
pop ds
ret
    

# Start the program at offset 0x7C00 using "org 0x7C00"
# At the end of the program put "times 510-($-$$) db 0" to fill up the rest of the sector with zeros.
# After you do the thing listed right above put "dw 0xAA55" which is a word value which tells the BIOS that the sector you were just working in is the boot sector.

If that isn't your problem, did you put anything into ax before you started putting the the value in it into the data segment and extra segment?