I'll offer this:
Back in 2001 I cycled from Calgary to Banff, up the Icefields Parkway to Athabasca, then back to Banff and west to Yoho.
The east-west bits (Calgary - Banff - Yoho) were all on the Trans-Canada Highway, which was fine for cycling on.

The Kicking Horse pass to Yoho was OK, not particularly steep, certainly not nearly as steep as a near-vertical bit of tarmac on the road leading in to Yoho Park, where I did have to get off and push.

There was a grand view of the big circular section of railway as it goes through the tunnels in the mountains to climb over the Great Divide.

I was carrying camping gear, 2 panniers rear, 2 front, and tent across the rear panniers.

I don't know anything about the Trans-Canada Trail, I was on a road-touring bike and never left the tarmac.

If you cycle that route I'm sure you'll enjoy it. The scenery is tremendous. On a bicycle you can stop anywhere to take it in. Not so easy in a car, or maybe even on a motorbike.
I remember the route from Calgary through Canmore to Banff, which was 2 days I think.
To watch the Rockies grow and rise up in the scenery so slowly, an almost imperceptable amount each mile you pedal, is an amazing way to travel into the Rockies. You won't experience that on any faster means of transport.
And the best ice cream in the whole of Canada is on sale in Canmore.

After Yoho I returned east to Kicking Horse. On the way down from there I found myself cycling right next to a train that seemed about 2 miles long, and was going the same speed as me as I cruised down the slopes back to Banff. It was doing 22mph, and we were side-by-side for quite a while. I could hear the train's whistle but I don't think they could hear my bell. (Well, I didn't have one anyway!)

Scenery wise, cycling over Kicking Horse was magnificent particularly as I could stop as often as I liked to take it all in. I think even on a motorbike you'd be limited to the parking spaces that aren't that frequent.

If you plan to camp, when I was there late August/Early Sept, all the campsites were closed to tents because of bear season.
Except tent camping was available in Canmore and Yoho. But not Banff, Lake Louise and north.

Cycling all around there on the tarmac roads is highly recommendable, I wouldn't have missed it for the world!

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TTR250 - London to Cape Town