There is a description of the North part of the Lake Washington loop in Wert’s Bakeries #84. He recommends the Juanita Hill because of all of the traffic on the four lane roads that are your other options out of Juanita. However, you can avoid climbing over the Juanita Hill by using the Sammamish River trail to go around the end of the hill as long as you can tolerate a few blocks of traffic with no bike lane.
If you are riding the loop counterclockwise you’ll approach Juanita Beach on Market (AKA 98th.) Stay straight on 98th instead of turning left on Juanita Drive. 98th swings right and becomes 100th. (Note that you can continue straight on this road – it changes into 96th or “Waynita Way” and intersects the Burke Gilman at the Golf Course.)
100th doesn’t have a bike lane until just after the crest of the hill. Just before the top of the hill take Juanita – Woodinville Way when it splits off to the right. There is a wide shoulder / bike lane for most of the way on this road. Turn left on 112th at the signal. (The unpaved Tolt Pipeline trail crosses this street and heads up a big hill to your left.) At a big Christian High School, 112th goes left and down a fast twisty hill. By the bottom it has become 108th and there is a stop sign at a “T” intersection with Riverside Drive. Right after turning left onto Riverside Drive look for trail access on your right. This trailhead puts you on the Sammamish River trail right at the bridge over the Sammamish River in Bothell. Go left on the trail to hook up with the Burke Gillman and your loop around the lake.
Instead of taking the trail at the bridge you can continue on Riverside Drive and it will eventually put you onto a trail that crosses the river on its own bridge and connects with the Sammamish River trail just before the Sammamish River trail goes through an underpass below 96th street. (This is just north of the golf course.)
Riding clockwise, one could continue on the Sammamish River trail past Juanita Drive. At the golf course, just before the underpass, turn right on Waynita Way and follow it up a hill and then down hill all the way to Juanita Bay and the regular route.
Alternatively, after the golf course go through the underpass and then, instead of following the trail when it bends left before crossing to the other side of the river, continue straight on a bridge signed “no jumping from bridge.” This fork of the trail will put you on Riverside Drive which you follow to 108th. (You can also stay on the Sammamish River trail, admire the chickens, and at the bridge back to the north side of the river look for the path leaving the trail to the right. This will put you on Riverside Drive just before 108th.)
Turn right on 108th and climb to the top of the hill. This is untested, but on the basis of descending it a couple of times I don’t think it should be too tough. The total climb is less than 250 feet and you don’t have to deal with the kind of traffic you have on Juanita Drive (where the climb is about 500 feet.) Once you get to the Christian School stay on 112th until you get to the light with Juanita-Woodinville Way where you go right. At 100th make a left and follow it as it becomes 98th. You rejoin the regular loop route at Juanita Beach park. (You’re going to continue straight on 98th past Juanita Bay park and up the hill toward Carillon Point.)