There are plenty of campgrounds, and you don't have to book in advance unless it's a national holiday (July 4th weekend, Memorial Day = last monday in May, Labor day = first monday in Sept). If things seem crowded you can book in the morning for that evening. I never book farther in advance than that.
Montana in general and Glacier in particular is definitely Not Flat. But Going to the Sun Road (glacier) is a long steady climb, around 4-6%, not sharp and steep. Bring your low gears though, because by long I mean like 10-15 miles. Most climbs are much shorter, and there's very little that's any steeper than 8%.
I have to share pictures to get you psyched. THis is from the KOA Campground road in St. Mary's (east side of Glacier):
And this is in Wyoming, near Cook City on Sunlight Basin Road, on the south/east route I posted: