If a healthy baby boy's eighth day of life is on a Saturday, that's the day his bris milah / circumcision should be performed if at all possible. While elective surgeries are prohibited on Shabbos, circumcision in its proper time overrides Shabbos. However, only the act of circumcision itself overrides Shabbos: if there was no boiling water available to disinfect the scalpel, the bris would just have to wait till Sunday.
If no mohel is available within walking distance, could he ride a bicycle to get there?
Disclaimer as usual -- for theory's sake only. Ask a rabbi first. (And please be sure your scalpel is securely stowed before flying off on your bike.)