You can always ride up into the park itself. It's beautiful, and if you park down in Three Rivers, you won't even have to pay the entrance fee. There is no bike lane, but the park-wide speed limit is 25mph, and since many of Sequoia's visitors are European, they have a more humanitarian view of bicyclists than your typical Texan or Arizonan tourist. Just be sure to bring at least a 39-25 along, because there are a few sustained steep sections, which make it a fun, fun, fun descent!
Also, check out the 245 going North of Woodlake. It starts out down in the rural, less attractive valley, but eventually goes up silly-string roads (that were deserted when I was there) in the trees.