Just a few years ago you could call the day before and get a reservation, but last year were stories of people trying to reserve a month in advance and finding it all booked up. With no shuttle service from Badger Pass to GP this year, I expect the demand on the shuttle from the Valley will be even higher. Let us know how it works out for you.
Note that it is a big bus from the Yosemite Valley Lodge to Glacier Point. It's a one way ride on the Glacier Point Tour, $27. The tour begins for the season in late May, but call that number JR gave you to learn the exact date.
There is not a free shuttle for any portion of this journey to Glacier Point.
If you're a friendly chatty kind of person, you might find another person or family who is willing to give you a ride up to Glacier Point, about 1 hour.
Thanks for both responses. We were able to book the bus tour for Saturday morning. Looking forward to the hike!