The best cleaner for bronze sculptures is plain soap and water. The best cleaner is just a little mild soap, like Ivory liquid dishwashing soap and water. Just avoid any soaps with scents like lemon scent or other additives that might have unknown consequences. If you have water "issues" in your area you might like to use distilled bottled water. All you really need to do is loosen the dirt from the surface.
For daily cleaning a simple wipe off with a dry dusting cloth, mico fiber or swiffer dusters is all your sculptue needs.
When a piece is noticeably dirty and not coming clean with dusting and wiping, follow these instuctions:
Add just enough soap to a small container or bucket of water - just so that it has some bubbles floating on top. Too much soap could leave a soap residue that will require more rinsing later. Then dampen a clean rag in the soapy water and wipe down the sculpture. If the piece has a lot of nooks and crannies or bird droppings, a soft toothbrush might be useful.
Once the sculpture is clean, rinse out the rag and wipe down the sculpture with clear water to remove the soap residue. Again, use the toothbrush with clear water to clean hard to reach areas.
Next, dry as much as possible immediately with a soft cotton cloth and then allow the sculpture to dry completely.
Once the sculpture is completely dry you are ready to begin waxing. It is best to wax an outdoor sculpture in the heat of the day as this allows the wax to penetrate the pours of the sculpture resulting in a wax coating that will last longer. The best type of wax to use is plain, clear, paste wax such as Johnson's Paste Wax. It usually comes in a can and is very inexpensive. Avoid automotive waxes as they usually contain other cleaners, etc. that could be harmful to bronze. But most importantly, car waxes tend to dry white, so if you leave any at all in little cracks or crevasses it will dry white and look terrible and you'll have to start all over again.
For darker colored bronzes I would recommend Johnson's paste wax or Renaissance wax. For lighter colors or multi-colored patinas I would recommend Treewax, Blue Label or Renaissance wax.
To apply, use a soft rag or an unused paintbrush to get into nooks and crannies. Apply a light coat and allow to dry. Most waxes are dry within 20 minutes. Then buff the sculpture using a soft cloth or clean shoe brush. A second coat is recommended for outdoor sculptures.