You might explain that BEDMAS is not the whole story when it comes to the order of operations. There is an operation called negation. It reverses the sign on numerical quantifies. It gives the additive inverse of any number, i.e. for all $x \in R$, we have $x + (-x) = 0$.
Unfortunately, most textbooks use the same symbol for both subtraction and negation. Some calculators use different symbols ( - for negation, $-$ for subtraction.) It should be fairly easy with a bit of practice to tell from the context whether a '$-$' symbol is being used as a subtraction operator or a negation operator.
The negation operator usually has a precedence that is less than that of exponentiation but greater than than of multiplication. So, we now have BENDMAS.
In the expression $-1^2$, we have two operations: negation and exponentiation. BENDMAS tells us to do the exponentiation first, then the negation to get a result of $-1$.