If the bench was originally constructed for outdoor use, chances are pretty good that the wood used is cedar or some derivative of cedar since oils in cedar are the best natural protective agent going. Problem has always been that cedar, as it exudes the oils over a period of time, tends to turn grey.
When new, one would leave the piece outdoors for about a month to let just a bit of the oil leech out before finishing. I have an outdoor bench with a back and arms made of this wood and have always used either teak oil (actually tung oil) or Spar Varnish for the finish. The bench turns a lovely shade of darker wood, but still retains the grain and shading. Both the teak oil and Spar Varnish are waterproofing and well as protection from harmful UV light.
The major difference between the two is that teak oil needs to be administered (wipe on, wipe off after allowing the piece to sit for about a day) at least once per year. It soaks into the wood making it a very good protective agent.
Spar Varnish, on the other hand, while still being an excellent prtotective agent needs only be applied once every 2 years or so. It doesn't soak in as far as the teak oil. It's brushed on with a fine 2 to 4 inch brush and allowed to dry... about 4 or 5 hours.
Note: fir wither application, it's best to brush on some warm water and let sit until dry and then sand the piece smooth with 150 grit sand paper to bring to a nice smooth finish. The bench should be sanded the same way just before using either finish after a year or so. When you do sand it, keep a small rag with a little bit of the teak oil or varnish on it (depending on which you use for finish) to rub the piece down to get rid of the fine dust left from the sanding...