Assess the situation. Each bridge and situation is different. If it is an extremely small bridge, like a small footbridge going over a creek, scaffolding may not even be needed. For a bridge you cannot reach from the ground, scaffolding will certainly be necessary. Take into account the height and length of the bridge, and if there are any points to attach scaffolding. All of these facts will be important for planning your specific scaffolding job.
Choose a scaffolding. You can set up scaffolding on the side of the bridge so it is supported by the ground. If this is not feasible, as most bridges hang high above the ground or water, you'll need to use a hanging scaffolding. Make sure the scaffolding you use is compatible with the bridge and plan you created.
Understand your scaffolding. There are many different types of scaffolding, and it is imperative you understand exactly how the scaffolding supports its own and your weight. If you fail to understand how your scaffolding is supported, it could mean collapse of the scaffolding and injury or death to the workers on it.
Have a fail-safe. If your scaffolding fails, you need a safety mechanism to help prevent injury. One tried and true method is to attach yourself directly to the bridge with cable and harness. Just ensure that what you attach yourself to is a part of the bridge that will absolutely not fail along with the scaffolding.
Consult experts. If you are new to bridge scaffolding, you will need to be in contact with someone who knows the field well. Every situation you encounter will be different, and by consulting an expert you will be able to judge those situations yourself in time. When you first start out, you may want to work alongside this expert instead of just consulting.
Evaluate your decisions. The best way to learn is to evaluate your mistakes and past decisions. Even if you did a good job, there is a possibility that you could have done it better. Think critically and always seek to improve your technique and you will become great at scaffolding bridges.