Particularly I use the ‘Olympic Connection’ service that connects Port Angeles to Olympia, Wa (links bellow and no weekends currently). This is a multi bus route that is serves this rural area. To help answer questions about this service, I've decided to write up a some basic ideas for hiking by bus on the Olympic Peninsula. I will only cover the options from west of Port Angeles to the south ending in Quinault.
I suggest leaving Port Angeles via Gateway Center on the earliest bus, but not to early that the tourist wont be around to pick you up when hitch hiking up the various park roads; since there is no free shuttle service to trailheads and most are 15 miles or so off of Highway 101. I personally utilize the 0930 Forks Bus (route 14), because it still gives me the ability to make some miles on the trail; after the bus drops you off.
Elwha Valley Trails: 20 minute bus ride from Port Angeles. Bike or Hitchhike around 5 miles to Elwha Ranger station. Various trail systems can be accessed from this point. Elwha Trail starts another 5 miles up the Whiskey Bend Rd. (check if the road is open) *travel cost $1.50 each way
Lake Crescent Trails: 30 minute bus ride from Port Angeles. Bike really not necessary, since the unofficial trialhead is right under Highway 101; at the designated bus stop for Barnes Creek. Most popular of these trails are Storm King, Marymere Falls and Barnes Creek Trail which leads to the Aurora Divide Trails and gives an expert backpacker access to the whole Park. *travel cost $1.50 each way
Sol Duc Trails: 52 minute bus ride from Port Angels. Bike or hitch hike around 14 miles to the Sol Duc Trailhead. Most popular of these trails are Sol Duc Falls and the High Divide Trail Loop (Seven Lakes Basin). An expert backpacker can access the whole area. A weary hiker can relax at the Park owned Sol Duc Hot Springs; for a non-modest fee. *travel cost $1.50 each way
Hoh Rain Forest Trails: 1 hour 40 minute bus ride from Port Angeles (includes the Jefferson County Shuttle Transfer layover). Bike or hitchhike around 15 miles to the Hoh Visitors Center. Most popular of these trails is the Hoh Valley Trail which accesses the Rain Forest and Mt. Olympus (High Divide can also be accessed from the Hoh) *travel cost $1.50 + .50 for Jefferson County Shuttle each way
Lake Quinault Trails: Roughly 4 hour bus ride from Port Angeles (includes the Jefferson County Shuttle and Grays Harbor Transit Transfer layover and travel times). Bike or hitchhike a various distance of 13 to 20+ miles of paved to unpaved roads. Most popular of these trails are Enchanted Valley, Skyline Primitive Trail and North Fork Quinault which is also known as the Press Expedition Trial. I suggest getting off the bus at the Lake Quinault Lodge via the Grays Harbor Transit at the Quinault Merc. *travel cost $1.50 + .50 for Jefferson County Shuttle + $1.00 for Grays Harbor Transit each way
Olympic Coast: La Push and Rialto Beach can also be accessed by taking the La Push Bus (5 mile hitchhike or bike ride is required from Mora Road). Then you can continue backpacking from Rialto to Shi Shi Beach. If you continue to bus south from Forks, Kalaloch Beach's can also be accessed via Jefferson County Shuttle. (no overnight camping on Beach is allowed by the Park, but you can stay in the Kalaloch Campground which is right off Highway 101 *check for reservations)
'Olympic Connection' Transit Links:
Clallam County Transit
Jefferson County Transit
Grays Harbor County Transit
Related: Public Transportation to Olympic National Park
Thanks for reading - Barefoot Jake