No, you cannot do bne subroutine instead of jsr subroutine because jsr means "return to jump".
The difference between this and conditional branch instructions is that jsr pushes the return address jsr stack, so the routine knows where to return. If you just go to the subroutine with bne , the return address is not saved, so the subroutine does not know where to return when it is done.
The answer in the cafe shows you the typical way you would handle this, you just need to translate it into PDP-11 operations.
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