What kind of riding are you looking for?
I used to do that trip a lot, but I haven't done the full trip for a few years now. The roads are all good via the main highways. The maximum speed in the National Parks (about half the trip) is 90 km/h (56 mph), but most traffic travels about 110 (68). The Bow Valley Parkway (Highway 1A between Banff and Lake Louise) is my preferred route through that part of the Bow Valley. There is also the 1A from Calgary - via Cochrane - to Canmore, but you're not missing too much by taking the #1 (Trans-Canada) instead.
Like anywhere, there could be weather issues. The most serious being a thunder storm or hail. We have had snow, at some point, in all twelve months. Usually though, if you're going to get any snow in the summer, it will be a wet flurry and there won't be too much to worry about. I would be more concerned about critters, especially if riding after dark (not recommended).
As far as facilities, this too should be no problem depending on the mileage you get. Once you get past Banff, there's gas, lodging/camping and food at Castle Junction (just east of where Highway 93 to Radium, BC, meets Highway 1), Lake Louise, Saskatchewan Crossing (where Highway 93 to Jasper meets Highway 11 - open from late March through ~October?), Jasper, Hinton, Grande Cache, Grande Prairie, and a couple of other spots.
If you are looking for some gravel roads then you could take the Forestry Trunk Road (mostly Highway 40) which is, IMHO, a far more spectacular trip - mostly because it will be much less travelled, although you may have to dodge the odd logging or oilfield truck.