Shasta Smith, 41, interior architect, star of the 2014 TV show “Red Hot Design” and owner of the Vintage Monkey motorcycle-restoration shop in Sacramento, Calif., on her 1972 Honda CB175, as told to A.J. Baime.

Sometimes, life is all about chance and timing. Recently someone asked me: If it weren’t for my 1972 Honda, would I be who I am today, where I am, doing what I’m doing?

I...