If you're on a budget, though, the easiest way to clean gym bleachers is to make a simple cleaning solution and go over the bleachers.
Sweeping
First, sweep the bleachers with a broom to remove any loose dirt, food, or buildup. Sweep either to one side of the bleachers, or for open bleachers, simply sweep the dirt down to the floor. Then, sweep up all debris on the floors and collect with a dustpan.
Making a Cleaning Solution
An inexpensive cleaning solution can be made from several ingredients. Distilled white vinegar is one of the best options, since it is inexpensive and will clean and disinfect with ease. In a bucket, mix two gallons of warm water with two cups of distilled white vinegar.
Baking soda also works as a cleaning and deodorizing agent--perfect for smelly gym bleachers. In a bucket, mix two cups of baking soda with two gallons of warm water, and stir to dissolve the baking soda.
Plain old liquid dish detergent is another inexpensive cleaning agent that will clean and break up film, food stains, and other grime that has developed. In a bucket, mix two gallons of warm water with four squirts of liquid dish detergent, and stir to combine the ingredients.
Cleaning the Bleachers
Cleaning the bleachers is quite simple from this point. You've already removed all of the loose debris, so a simple mopping will take care of the rest of the problem. Dip a mop in the solution of your choice, wring out excess water, and run across the bleacher panels, working your way from the top of the bleachers down to the bottom. Continue until you've reached the bottom of the bleachers, and let them air dry.