Sandy -
You definitely need to eat to support your cycling - and it doesn't matter whether you're riding on or off the road! You'll need to figure out how much food your body needs before your ride; what works for me may or may not work for you.
I commute to work by bike in the summer. And maybe hearing about my commuting by bike eating habits will help your thought process. My commute is usually about 18 miles in the morning and 20 to 24 after work. I leave the house on my "ride to work" leg at about 6 in the morning. Before I ride, I eat breakfast - usually a bowl of cereal with fruit (banana, strawberries, blueberries this time of year), and a piece of toat or a toasted (frozen) waffle topped with peanut butter. When I get to work I usually grab a cup of tea and some yogurt. I have a mid-morning snack, lunch, a piece of fruit in the middle of the afternoon, and usually an energy bar a little before the end of my work day. I figure I need the extra fuel for my ride home. Hmmm - when I read this, it looks like I'm eating all day! I eat a light dinner soon after I get home too.
So - eat!
Oh, and there are two sports nutrition books that I find helpful. They are Nancy Clark's Sports Nutrition Guidebook, and Liz Applegate's Eat Smart, Play Hard.
--- Denise