Hey Jay, did you post on photo.net too? if so go there.
I'm not being a jerk when I say that there is no best time! It's always in motion up there and it's best when I'm there! That said, I like early to mid August and all of september are my favorites. I loved it in february this year when I wen through on my way to Jasper to photograph wildlife, I also love the cold and the snow. Keep in mind that the flora in alpine areas change so fast that one day the flower you want is there and the next it's gone but replaced by another. the growing season is so short that from one week to the next the flowers are different. with some scouting you can find a larger range of flowers, but you have to know what and where to look. get a good buck on albera rocky mountain flowers.
If I were you Id go in early to mid august. AND prep for any weather. I dont forcast the wather but I can tell you that you could get hit with rain, sun and snow all in the same day. Dont be foolish and head off up the trail without proper gear.
Most of all have fun.
by the way go check out photo.net under the nature sectio where the same question was just asked last night. . .