This says nothing on water.
https://www.nps.gov/glac/planyourvisit/conditions.htm

But that page says very little, so that does not really provide any assurance that water is available. You should be able to ask at the gate when you enter the park about water. If you see a parked shuttle bus, the bus drivers probably would know if water is not yet available at various locations.

When I was there in early July 2012, I am pretty sure I topped off my water bottles at a drinking water fountain at Logan Pass. But there was no food at Logan Pass, other than maybe candy bars. This early in July, the park staff might still be getting the infrastructure up and operational at different park facilities.

I suspect that water has to be available at any campgrounds before the campgrounds are opened, otherwise the toilets would be a disaster. I can't imagine they would try to operate with just contracted port a potties.

I liked the hiker biker site at Sprague campground. Less crowded than Apgar campground hiker biker site, but Apgar was close to the store, restaurant, etc. I stayed at Apgar one night, then Sprague for two nights.

Good luck on this. I assume you already are familiar with the cyclist restrictions for time of day on Going to the Sun Road, etc. The restriction times and locations are different than when I was there 12 years ago. If you are not, they are on this page:
https://www.nps.gov/glac/planyourvisit/bicycling.htm

The climb up Going to the Sun Road is a steady gradient with almost no variation in slope. I stopped at a pullout every 250 to 350 feet of elevation gain on the uphill climb for 3 to 5 minutes at each stop, just to make the climb less tedious and to take photos, etc. That made the climb more relaxing.

I hope the weather is as great for your visit there as it was for mine. Have a great time.