Disclaimer: Any method you use to do this, especially with a consumer GPS unit, is going to be an approximation at best. If you truly want to know where the boundaries are, you will need to locate property pins/corners which might require a metal detector. Your best, safest option is to hire a professional land surveyor.
No, those are not lat/longs in the description. Those are bearings and distances. What you have is a metes and bounds description which locates a point, gives bearing and distance to the next point, and so on all the way around and back to the point of beginning (known as a traverse). Such descriptions usually, and in the case of the example you give, refer to the Public Land Survey System (PLSS) in the US.
To locate a section corner you'll need to either estimate it from data or find a benchmark. For some states you can locate a GIS version of the PLSS grid - see PLSS shapefiles - alternative to geocommunicator.gov? But do note those aren't surveyed - some points are (control network) and the rest are calculated to fit. You could also check with the county to see if they make their survey control network available. This would have actual surveyed corners and locations of benchmark monuments, possibly with lat/long coordinates already provided. You'd have to locate the nearest benchmark and work your way to it - the plat survey should have note on it somewhere of such a benchmark. If all you have is the description, you're on your own. And since you'll be starting at a quarter-quarter corner, you're unlikely to find a monument right there (they're usually sections or quarters at best).
Once you find that point, from your example the description starts immediately. In some cases there are commencement calls that get you to a true point of beginning, and then the shape starts. From there it's an orienteering exercise.
To get all this into GPS coordinates, you'll need to know at least one point's lat/long and work out the rest, or plot the description and unproject it to a geographic coordinate system. A related question, though for a different country, can be found at Outline a plot of land on a map. You don't mention what software you're using or have access to. If you specify something, more help could be given.
Honestly, your best bet is to go to the county GIS website (per your descripton). Using their online map application, you can get a pretty good idea of where the parcel is and possibly turn imagery on to get some landmarks to use in locating it. Their section grid is on by default, zoom in far enough and you'll be able to see the labels to locate 03-25-2E per their labeling scheme. Looks like it's on the north end of the City of Bainbridge Island. Since I can't see the full description, nor do I know exactly where the quarter-quarter corners are, I'm guessing it's one of the parcels in the vicinity of the one outlined in green below. The SE corner of the SW4 NW4 is somewhere around the bottom right corner of that parcel. I've outlined the section in red, because the gray dashed line they use is kind of hard to see. If the documents you have include a parcel ID number or address, you can look that up directly in the system.
You can also use that page to identify the correct parcel, and then pull it up in Google Maps where if you right-click a point and choose What's Here? it will give you the lat/long coordinates of that point. So you could get a rough idea where the corners are and then get ballpark coordinates to use in your GPS. Which remember a consumer grade unit is only going to be accurate down to about 3m anyway.