Hm, I'd say the environment can matter quite a lot. My own bike is a carbon "race" bike with 21mm tyres and yet I'm sure I get in that "zen" zone practically every time I ride it. I ride it exclusively in the countryside, on mostly secondary roads.

I sometimes ride a bike with fatter tyres in the city and I never get in that zen state. Probably because I have to stay very alert, even when riding on bike paths separate from the street.