I'm not really opinionated about whether or not you should do algorithmic stuff in the interview, but I don't agree with your reasoning here.
I see chatter about how most problems can be solved with google and your CS teacher lied to you (usually on reddit, less so on HN). My experiences have not matched this. I'd estimate that a good 40-80% of my problems don't have a solution on google. It's pretty rarely an algorithmic problem though.
If you're playing that game, are there reasons that you'd ever be copy pasting sorting algorithms from the internet? Why bubble? Don't most programming languages have libraries available to help (especially python)? I work in an area with very little sorting, but I can't imagine myself doing that in a higher level language, or even in C.