How long will it take? In western Washington it can rain anytime. June is often rainy, though can be warm and sunny too. I think the optimal time for good weather up there is July-September. It can snow in Montana anytime, but the odds are you'll get good weather in July and August. I think if I were doing this trip (it sounds fun) I'd start in late June. After you get across Steven's Pass, which way will you be going? Sandpoint, Idaho? Glacier N. P.? I've ridden a lot in that neck of the woods (though not as far east as Livingston.) It's wonderful country! Have a great tour!