Yes, null terminator for dos string is this -> $.
Maybe this will work:
section .text
org 0x100
start:
mov byte[var1],'A'
mov byte[var1+1],'B'
mov byte[var1+2],'C'
mov byte[var1+3],'$'
mov ah,0x9
mov dx,var1
int 0x21
exit:
;mov ah,0x8
;int 0x21
mov ax,0x4c00
int 0x21
section .bss
var1: resb 10