Thunder Creek Trail appears to be in North Cascades National Park - - which is all designated Wilderness outside of the few developed ranger stations/campsites/etc. The NPS page on the trail indicates that the only uses are hiking and equestrian. Without coming right out and saying it, the Bicycles page seems to indicate that bikes are only allowed in campgrounds and on the highway/roads. They also steer mountain bikers to pages on the Methow and the Okanogan-Wenatchee National Forest. I think you're out of luck on that one.