The distance from Pumphouse to Catamount Bridge is 34 miles. Add six more miles to Derby Junction. You cannot do it in a day, but at this level it is a solid, long two-day trip. To cut down milage, try Radium to Catamount. There aren't a lot of big rapids, but there aren't a bunch of other rafts either.
Here is the crux of your trip. There are no shitters below State Bridge. If you camp at Windy Point, you will have plenty of company in the form of car campers--and in my experience the Windy Point campsite has some of the sketchiest people I have ever met. If you can get to the Twin Pines site, you will find a really cool campsite. Unfortunately, the trains are VERY active across the river, and they are close. On the upside you will have acess to unbelievable fishing, fantastic hikes and a great chance to see wildlife (especially Mountain Lions).
From there down its an awesome float with incredible fishing.
Derby Junction rapid is a different story. You can flip a gear boat in the hole. I've seen it with my own eyes. Unlike all the other rapids from Pumphouse down, I "rig to flip" for Derby Junction. For that reason, I've never been a fan of running that rapid after a lazy multi-day float.