The Backdoor 5.8
The Backdoor 5.8 is fairly straight forward 4-pitch link up. P1: You climb a route on Garden Wall (any route will work, but make sure you end up on the anchors on the farthest right side). Then make a short traverse to the right over to the left side of P-Wall (the only awkward part of the climb). Your belayer will belay you from the Garden Wall anchor. P2: Climb up Garden Party (.7). This route is on the extreme left side of P-Wall, at the top of the gully. You can only really get to it from Garden Wall. After you climb it, from the bolted anchor at the top of the 2nd pitch, gather your rope and scramble back to the base of a steep wall (100' or so of walking to get to the base of pitch 3. P3: Climb Sunnyside (.8 crux). From those anchors at the top of pitch 3, climb easy 3rd-class slab to the base of the steep wall above (I wouldn't really call this a pitch, but it's necessary to move up to the base of Hobbit Arete). Bring your belayer up so they can belay there. I've always just used the first bolt of the next pitch as a belay anchor (just use a 6' bight of rope. Then climb the short and obvious Hobbit Arete P4: steep face with a sharp arete to the right (.7) to a belay. Then pack up your rope and scramble the last short distance to the top where the hiker's trail ends at the base of the summit block. You can climb Flakes to Fresno (.8) if you want to really climb all the way to the top.
Historical Note: After I put up Garden Party in 2008 with Klis, I knew that after I added one more pitch above Sunnyside 5.8, I could climb to the top of Bishop Peak instead of hiking to the top. So I did. The reason I've posted this as a "route" is because two of the pitches were added specifically to create one long route to the top. It's not just a random link-up but done to create a 4 pitch adventure route.