Mt. Princeton Hot Springs Resort, can you say 'relax'?
This trail is mapped from north to south direction, in alignment with the rest of the Colorado Trail segments, the main description is per that same direction, although going the opposite direction (from south to north) is easier from a climbing point of view.
Start at the paved parking area at Harris Gulch, on the north side of CR306, just west of Rainbow Lake. Head south out of the parking lot, cross CR306 and the bridge over Middle Fork Creek. This first section of trail is fairly mellow, slowly downhill along the creek and Rainbow Lake, before it pitches up, after crossing CR344, going to CR343.
Cross CR343, approximately three miles in, and get your technical climbing game on. This is one of those older, worn-out sections that will require some walking in a good number of spots, then has some easier sections, then more steep (barely rideable). Luckily, this section is less than two miles long. The last climbing turn provides a great view back of where you started, and of Mt. Yale. Almost at the top.
Enjoy the next 5.5 or so miles of great singletrack as you pedal along, up and down, across a few creeks, with a few short steep sections (typical CT stuff, going in and out of creek drainages), one or two that might require a short hike-a-bike. Generally, this section of trail is good fun though, with some great views of the Arkansas Valley, while going through a few aspen along the way.
Approximately 10 miles in, this trail joins a jeep road, CR322. The road goes (partially) up Mt. Princeton. Stay left, go DOWN the road. Careful with the loose over hardpack surface and the ruts in this road. Pass the ranch and continue rolling down CR322, which is now paved. Take a sharp right onto CR321. At the bottom, turn right again onto County Road 162 (Chalk Creek Dr.)
, all paved. The Mt. Princeton Hot Springs Resort can be found at this intersection. Be aware of the traffic on this road. Again, turn right/west.
Look for CR291 or Bunny Lane on your Left. Continue straight until you run into the Chalk Creek TH, the finish of 16 miles of CT Segment 13.
This section of the CT is also good in the opposite direction, as an out-and-back from the ranch at the bottom of the jeep road CR322, turn back at 6.5 miles in (at the climbing turn). Or as a shuttle ride, riding the same northbound direction.