How to temporarily cover blue hair with brown?

I don't think there is any way you can cover up blue with brown and then wash out the brown and still have that blue hair underneath. In my country we have some dyes that can be washed out after 3 washes as if your hair was never even dyed, but those only do well on natural unbleached hair. once I tried to put purple on top of my pink and I could never go back to pink without stripping colour and putting pink back.
I think You can only cover up that blue for one day with a wig, or by putting up your hair in a bun and wrapping it up so the blue is not seen.
Anyway, good luck with your interview.  *1*

Yep, a wig is really the only option. Anything that will actually cover the blue will stick around for more than a few washes and may never fully wash out.

Or just go to the interview with blue hair, but mention that if their policies don't allow unnatural colours, then you'll dye it.