This FKT is from TH to peak - the generally accepted candidates to get from the TH to shadow canyon are mesa trail (with or without the recognized "mesa cutoff"), homestead trail, or towhee trail, but you're welcome to stick to any OSMP trails you like.

Bear is really a subsidiary summit of South Boulder Peak, but with a satisfying summit with terrific views.  The standard route starts from the Cragmoor TH, at the west end of Cragmoor Road, and ascents the Cragmoor Connector, North Fork Shanahan and Fern Canyon trails to the true summit of Bear Peak, where there is a benchmark.

This route is in City of Boulder