A loop that I’ve done before is to start at the BV gas station and head up to the lake. Near the dam, cross the street you’ll find a trail that takes you up to the big turn where they park the snow cats. Then proceed up the dirt road to the top of Koala and continue up to the top of Bear. From the top of Bear, go down West World and you find along the dirt road and find the mid slope trail that takes you over to Corral Ridge. Continue on and depending on how far you want to go you can take a left on 7N35 which takes you back to CA-4 via Corral Gulch. Or, if you want to keep going, don’t take the left and follow the trail to Bear Trap Basin. Which loops around and comes back to 7N35 for your exit.
Attached is a crude .gpx file I made showing the route. Note, there are some extraneous lines so be careful using this solely as your navigation.
Well, there’s the Wheeler Lake trail if you can find the other way back. Go in at Woodchuck Basin, takes you up a summit near Mt Reba, drop down the other side and you get to Wheeler Lake, which is lovely. Most people go back the same way (~ 7 mi RT), but I’ve heard there is another trail up and over to the northeast, and I think we saw the traces of it from the summit. This could make it a loop, probably about the right distance. However, even the main trail was somewhat damaged over the heavy winter, so I suspect the “northeast passage” is even more difficult this year.