Varenna to Pontresina ( or a nearby village) is a great trip---we went the other direction last September and loved it. We have spent a lot of time in Switzerland, hiking and riding trains, but that ride over Bernina Pass is the best.
Riding the whole Glacier Express the next day would be "too much train" for me. I am going to go out on a limb and suggest you break the journey with an overnight someplace you will not read about in Rick Steves guidebooks. But it is a car-free village high above the valley with gorgeous views from the village and even better ones from the peak above town ( reached by a gondola).
The town is Bettmeralp, which you reach by cablecar from the town of Betten on the Glacier Express route. Your Swiss pass will cover the ride 4000 feet up to the village in the cablecar. If you are on the actual Glacier Express train, it will not stop at Betten, so you must continue on to Brig and backtrack from there (only 10-15 minutes).
Browse these photos and see if you are interested, and if so, I can go into more detail.
http://www.aletscharena.ch/destination-en/photo-gallery/
