From Ouray, drive south on US550, up the switchbacks out of town, through the Uncompahgre Gorge, and up the four switchbacks into Ironton Park - a surprisingly large, flat valley area that extends for over two miles. Driving south, the Hayden Mountains will be on your right (west). Though it's not very visible from the highway, there's a road that extends all along the west side of Ironton Park that goes in and out of trees and stays right at the base of the mountains and on the edge of the open meadow. This route will utilize that road.
Drive to the south end of Ironton Park and the very large tailings pond where a secondary, gravel road turns off to the right to access Gray Copper Gulch and Corkscrew Gulch. About 1,200 feet beyond that road, there's a pullout on the right (west) side of the highway with an old cabin. See coordinates below. Park here for the trailhead.
There are no national forest campgrounds along US550 between Ouray and the turnoff near Silverton for South Mineral Creek. There are however, a number of primitive sites, many of which are fully occupied on weekends. The previously mentioned road that turns off for access to Gray Copper and Corkscrew Gulches leads to a nice camping area in the trees with a number of sites. These tend to be occupied by trailer rigs.
If you drive south from the trailhead about 2,000 feet, there's a dirt road that turns off on the left and drops down into the river floodplain. There are numerous sites all through here as well. There are also a few other primitive sites along US550 as it departs Ironton Park heading south. YOu can also find some primitve sites off the highway near the summit of Red Mountain Pass.