Going NoBo, they'll probably be in CO around the Breck area roughly mid-June IIRC.
Depending on the snow year, there could be a LOT of snow still (though, this year is looking to be lighter so far in that area).
If you absolutely want to join them in early August or so, they'll be more around Yellowstone.
So, I guess the next question is, when do yo want to join them? :)
Pagosa Sprgs, CO to Rawlins, WY is probably the easiest stretch in terms of logistics but may not work for your timing.