I assume you've read what the park says about the hiker/biker sites here:
https://www.nps.gov/glac/planyourvisit/ ... MP_5204139
Have you tried calling the park to ask them directly how a late-arriving biker might check get a site and what happens if those sites are full and there is no "regular" site available?
The main number is (406) 888-7800 . They can probably transfer you to one of the campground officials.
If you can't get a clear answer from them, I'd just go ahead and reserve a car campsite (looks like there are some still available) for your first night and then switch to the other hiker/biker sites (first-come, first-served, I assume) the next day. The peace of mind will be well worth the extra $15 or $20 bucks.
Good luck!