I would recommend that you always carry a little cash for a bus fare (or taxi if there aren't buses that run in your area). If you get a flat or have a spill or something, depending on conditions it may just be better to get home first and assess/repair the damage later.

It's not strictly necessary, but it's good to have a backup plan. I'm one of those cautious types, so I keep some singles in my repair kit and my change purse in my lunchbox.