As I mentioned above - there are backcountry hike-in / bike-in campsites.
The ones relatively close to the parkway are usually not destination sites.
So, there are more likely to have openings - even same day.
They also tend to be trailside and not especially spectacular.
All backcountry sites I have used have either bear boxes or bear poles.

The one drawback is you have to pick up your permit in person.
That's so you watch the backcountry practices video which is required.
Northbound can be a problem with sites in south of Banff.
But southbound you can stop in as Jasper park office right at the start.
Last time, you could get permits for both parks in any office.
Offices are at Banff, Lake Louise, and Jasper.
(There's only an info booth at Icefields.)

Since nearly all riders are coming from or headin into British Columbia -
Plan to stay at Kinney Lake backcountry site in Mount Robson Prov. Park.
You can bicycle in on the Berg Lake Trail. (7 km.) Truly spectacular.
Permit required - park office near trailhead.
Then its 90 km from the trailhead to Jasper townsite.

https://nrs.objectstore.gov.bc.ca/ku...fce7c2b377.pdf

In Jasper there are lots of homes that rent small rooms and a hostel nearby.
The Saturday Night Lake Loop backcountry sites are usually taken.
The nearest site south is along the Whirlpool River via Old Hwy 93.
(Bikeable fire road to campsite, moderately challenging)

Fortress Lake / Chaba Trail is also a fire road - kinda rough, but bikeable.
What's nice is that the Sunwapta Lodge is at the trailhead.
So, you can have a meal before heading in or breakfast on the way out.
Big Bend is 6.5 km in.

http://parkscanadahistory.com/brochu...ide-e-2018.pdf

You would have to hike in to Hector Lake since the trail is not bikeable.
It is lightly used and there are canoes at the lake. (Or there were)
I didn't have a PFD and was alone so I used better judgement.
(On of the few times that I have done such.)
Only 1.5 miles off the highway.

Nearby Mosquito Lake front country campground is the last to fill for some reason.

Red Earth Creek campsite is very lightly used - halfway between Castle Jct. and Banff.
Then it's a kinda uphill slog for 6 km. Small, heavily wooded site.
Also, you have to use the Trans Canada Hwy #1 to access Red Earth.

If you are planning to continue on to Kananaskis - then you should consider the Spray River Trail.
It connects to Spray Lakes / Smith Doreen Rd. Popular cycling trail.
There is a lovely backcountry campsite 6 km south of Banff, but hard to come by.

http://www.parkscanadahistory.com/br...try-e-2017.pdf
(The older map shows bikeable trails more easily)
http://www.parkscanadahistory.com/br...ry-e-c1999.pdf

Kananaskis is where Albertans go to escape from the hordes of tourists.

Jama

Pic - Kinney Lake at Mount Robson Provincial Park