Making Bear Basin part of your trek through the Winds will potentially provide you with a life-changing experience. This place is the most beautiful place I've ever seen.
There are many ways to get to Point 13,062. If you are doing your trek in the northern part of the Wind River Range it makes sense to start at Green River Lakes. From Pinedale, Wyoming head west out of town on US 191 for 6 miles and turn right (north) onto Wyoming road 352W. The pavement ends soon after the small town of Cora. Continue for 25 miles from US 191 and continue 18 more miles on the Green River Lakes Road until the road ends at the Green River Lakes campground. This road is passable for any vehicle although it gets very wash-boarded.
From here your choices are almost endless, although you have only three options to choose from right at the start. You could take the nice trail south past the Green River Lakes for 14 miles to Three Forks Park. You could conceivably hike the trail up to the Clear Creek Natural bridge but then continue onward through horrible blowdowns and bush-whacking to Clear Lake and beyond to Bear Lake. I would highly discourage this unless you get pure enjoyment of self inflicted torture. Your third option is to take the trail northwards from the campground. This long trail then turns east and follows the Roaring Fork around the north side of Osborn Mountain. This is the route I took to start my trek and it was nothing short of spectacular.
If you take the trail heading south, your trek will start easy but once you get to three forks park you have to leave the trail and follow a boot path through the marsh and grass to the Green River. Find a shallow place to cross the bright green waters and start the grueling ascent of Tourist Creek. I can only imagine how hard this ascent is as I descended it on my trek. Come prepared with lots of food!
Continue ascending Tourist creek. The final climb will be up a loose and very steep boulder slope to a low point on the continental divide just north of Pedastal Peak. From Here you can follow the divide north until you reach Point 13,062.
If coming from the Roaring Fork valley, continue until the trail ends. Beyond this point you are entering true untouched wilderness. Ascend to Native Lake and continue to Crescent Lake. Published maps show a trail leading all the way to Crescent Lake but that isn't true. From Crescent lake you can either hit the divide right away and traverse south over Downs Mountain or do a contorted traverse over many small ridges and through many valleys to the west of the divide.
Doing this, you will pass by many spectacular lakes including Daphne Lake, Bear Lake and Bear basin. From bear basin, you can hit the divide by climbing up the obvious drainage at the basin's east end. There is a waterfall you'll have to climb around on the south side that gets really loose. Once above this waterfall continue up the drainage as it curves left (north) and climb around another waterfall on the west side before the terrain flattens out just below Downs Mountain. From here you can climb the talus to the summit of Downs Mountain and continue south to Point 13,062 on easy terrain along the divide.