There are various coatings you can apply that will make the deck and bridge non-slip. Most have fine sand or some textural material included to provide better grip. But the deck must be clean and dry before application, so you will have to wait until after winter before you can apply.

In the meantime, you might use non-slip tape applied as needed. This is often used on wooden steps to prevent them from becoming too slippery in winter rains but will work equally as well on a deck or other wooden surface.

I'd give it a good cleaning using Oxiclean to get rid of the plant growth on it, for starters.

I was thinking the same as Wood's Shop that it probably need a really thorough cleaning, including scrubbing. I imagine you have some growth on the wood that's making it more slippery.

Also, have you talked to the landlord about the issue? If I was a landlord and my tenant was in danger of a slip and fall, especially on a bridge without a railing, I'd worry about liability and want to work on a fix for my tenant.

great suggestions everyone! and yes! I should be bringing it to the landlord's attention! thanks.