Destination Expert
for Jasper, Jasper National Park
Peak bloom time for subalpine areas is July 15 to Aug. 15, but of course, so much depends on the weather. Last summer, for instance, was much colder than usual, and bloom times were at least two weeks later than normal. However, even outside of the "peak times", there are flowers blooming. In the montane (lower elevations), there are many, many species of flowers blooming by mid-July.
I have never booked the bus to Lake O'Hara, but my understanding is that it is best to phone starting at exactly 8 am (MT) to make a reservation, 3 calendar months ahead of when you want to go. I've heard that sometimes, the available seats are sold out by 8:15. Cancellations and no-shows are also possible, and I've heard of some getting seats by showing up at the parking lot. There are other nearby hikes available in Yoho NP, so it's not too hard to switch to "plan B" if you aren't lucky enough to get on.
Six miles is about 10 km - lots of hikes fit your requirements. On your way to Jasper, you may want to stop and hike either the Parker Ridge trail or the Wilcox Pass trail, approx. 5 km and 8 km respectively. (Wilcox = 4 km to the pass marker as turn-around point).
I think one of the attractions of hiking at Sunshine is that it's an easy way to get up to a higher elevation... this is also one of the attractions of hiking near the Icefields, because you are already starting up fairly high (in the subalpine), so it doesn't take as much work to get up to treeline and above.