I live in La Crosse and am very familiar with Hwy 33, esp. the western half. This weekend I'm biking down to Madison, using Hwy 33 for most of the way.
Hwy 33 is bikable. The worst stretch was near the end, between La Crosse and St. Joseph (it still shows as red on the state maps). That stretch has now been redone with a v. good shoulder. No problems at all.
Between St. Joseph and Reedsburg is OK. Traffic near Ontario is always light. Near Cashton and Ontario you'll see many Amish. Between Union Center and Reedsburg, if the traffic is too heavy you can always jump on the Trail. The Trail is pretty typical for Wisconsin. I don't usually ride on it, but it can be nice break. Traffic is mostly local with few semis, mostly milk trucks and the like.
While I would not want to bike it everyday, it is bikable. There aren't many alternatives unless you want to get into the hills and valleys (with the necessary climbs). Be visible and you won't have any problems, at least I never had in the six or so times I've made the trip.
If you want a neat way in to La Crosse, turn right (north) on Cty. F, just outside of La Crosse. The hill descent is much funner (but more difficult) than coming in on Hwy 33. It will also take you right in on Main Street, convenient to the University, etc.