The best way is to use treated lumber or naturally resistant wood like cedar for the decking material.
Sounds like the bridge is already built so you will have to use a brush on treatment. You can pressure wash, but then it is best to let it dry out again to allow the preservative or stain, which is usually oil based to soak in. I would recommend a solid stain to give some UV protection also to the wood. Most of the wood preservatives use a mixture of petroleum oils with wax added for repellant. Depending on your climate, you might be able to make it last for 10 to 15 years.
Another option would be to put "roll roofing" over it. The granular surfacing would also make it slip resistant.