Hey Wren - welcome to the Northwest and you've just come from the Land of Lance - wow!
I'm up in Edmonds, just north of Seattle, but have done a few rides in the Bremerton area. Yeah, anytime you're out on the peninsula or on 1 of the islands, you should expect hills...there are a couple of hills on a ride out of Silverdale I did in 2001...that were killer...I heard plenty of moaning, cursing ( along with my own!) and more from even the gnarliest riders as we climbed up out of DeWatto and then Tahuya (think I got the spelling right)...anyway, they're both south of you, before we headed back along the nice flat scenic shore road...it was part of a century route of the well-supported ride called the Triple Trident ride in June. Each route had an 11 mile loop thru the Bangor submarine base to make it a very unique ride for sure.
There are plenty of gorgeous routes all over the Puget Sound/Western WA area, so let me know if you're interested in riding sometime and it'll be fun to encourage you on!