Do you remember the first time you rode your bicycle -- really rode it, without training wheels or someone holding on to the back to help you keep your balance? It was an exciting moment. You probably felt grown up, proud of yourself and free. All of a sudden, you had a new way to get around.

Riding your bike can still be thrilling, even if you are an expert at it now. It's fun to race along, especially downhill. It can even be fun to struggle up to the top of a steep slope.

Bike riding is one of the most popular things to do for kids all over the United States -- and all over the world. A study by the U.S. Public Health Service called "National Children and Youth Physical Fitness" reports that children up to the age of 9 say bike riding is the number one outdoor activity they spend time doing outside of school.

So there are lots of kids riding bikes out there. But as you probably know, not all of them obey the rules of the road, or follow good safety practices. It can be tempting to show off on your bike, or to try daring tricks like the stunts you see on TV or in a movie. Don't! Fooling around can cause serious injuries.

This week is National Bicycle Safety Week. If you write to the National Safety Council, Dept. PR, 444 Michigan Ave., Chicago, Ill. 60611, they will send you a free pamphlet about bike safety and rules of the road. In the meantime, whether you ride a sturdy utility bike, or a fancy 10-speed racer, use your common sense and follow a few basic rules to stay safe:

* Be sure your bike is the right size for you. Measure your inside leg, from your crotch down one leg to the ground. Then measure the bike, from the place where the seat post slides into the frame to the center of the pedal crank. The second distance should be 10 inches less than your inside leg measurement.

* Adjust your seat to the right height. When you're in the saddle, you should be in almost a standing-up position -- even though you're sitting down. That way, your leg will be almost straight when your pedal is at its lowest point. You won't feel as much strain if you ride in this position.

* Never ride double or hitch rides on cars.

* Obey all traffic signals. Keep to the right of traffic. Signal when you plan to turn. Walk your bike across busy intersections.

* Never ride against traffic.

* If you're biking with a group of friends, ride in single file.

* You should have reflectors on the front, rear and sides of the bike. Use reflecting clothing and install a headlight if you plan to ride at dusk or in the dark.

* A water bottle mounted on a bracket on the bike frame is a good idea if you plan a long trip. You sweat when you ride a bike, but the air rushing past dries you quickly. You may not notice that you're losing a lot of liquid. Replacing lost liquid by drinking helps keep you from getting exhausted or overheated on a long ride.

* Don't load your bike up with a lot of unnecessary accessories or decorations. They can throw the bike -- and you -- off balance.

Always wear shoes when you ride your bike.

In additon to getting you where you want to go, bicycling is excellent all-around exercise. When you ride, you use lots of your muscles and help them grow strong. Only swimming provides a better workout for all the parts of your body. For a really great workout, try riding your bike to the swimming pool. And ride carefully so that you get there safely. Tips for Parents

Your children may object that helmets aren't fashionable bicycle attire. But studies show that they can significantly cut down on the seriousness of bike-related injuries.

Bike mishaps are one of the most common causes of childhood head injuries. Some of these injuries result in death. In Dade County, Florida, physicians studies 173 fatal accidents involving bikes and cars over a 23-year period. The study was done for the Insurance Institute for Highway Safety. They concluded: "Had many of those cyclists with fatal head injuries been wearing helmets, they probably would have survived their other injuries . . . The prominent role of such injuries in the deaths of younger cyclists suggests that this group's survival would be especially aided by the use of helmets."

Try including a helmet in the deal when you get your child a first bike, or a new bike. A life could depend on it.