About the only time you don't want to go is June (that's actually mid-May to mid-July). Some years the melt starts late, etc.

Bozeman is a good central location. You can also head a little further east past Livingston to Big Timber for the Boulder River, a wadable freestone, float the 'Stone, or find a few other smaller streams in the Stillwater Drainage (another wadable freestone).