What is the past form of the structure "used to"?

We generally change the tense of the verb and shift back when reporting something (unless it’s still true, has just been said, or is a scientific fact). For example, "I was sitting in the car" changes to "She said she had been sitting in the car". When backshifting, how should we change "used to" in the indirect speech?

For example, when we are reporting the sentence

"I used to play volleyball when I was a kid"

it changes to an indirect speech and becomes

"She told me she ____________ play volleyball when she was a kid"

a) used to
b) had used to (odd, I think)
c) ?

Is "used to" similar to other modal verbs such as "should" and "would" with which we don’t do the backshift in the reported speech?