This is the only route to the summit of Bonneville Mountain that looked feasible to me. It's a fairly easy class 3 scramble, but it can be loose and exposed in places. The route starts from Jewett lake.
See the Getting There section on the Bonneville Mountain main page for directions to Jewett lake.
From Jewett lake you will head northwest toward a ridge coming off of Petes Point's north ridge. You will ascend this
redish looking scree to the low point of the ridge between two large rock formations. You will drop down the other side of the ridge, cross the basin below, and head up the main ridge. See this
Once you achieve the main ridge you just follow it all the way to the summit. There are a few rock pillars you must bypass, this is most easily done to the left (west). The summit register is on the east summit (the darker pointy one). Descend the same way you came.