In reply to Derry:
I can't see any very good options for cutting costs if you want to do what we did, which is go from the Tschierva over the Biancograt and down to the Rifugio Marco e Rosa, then across the glacier plateau to the Diavolezza.
You could camp instead of using these huts, but then you have to lug a tent over the Biancograt, which would spoil the fun and slow you down.
Or you could try and go super-fast, maybe cutting out one of these two hut stays? But it's a long walk from Pontresina to the Tschierva, and only a little of it could be mountain-biked. And it's also a long walk from Piz Bernina to the Diavolezza cable car, unless you have skis.
The Marco e Rosa would be the easier one to cut out. Just start really early from the Tschierva, and move quickly, and don't be surprised if you miss the last cable-car down!
But I don't advise this. The Biancograt is a fantastic route and if you do it more than once in your life you'll be really lucky, so my advice would be to savour it--and to grin and bear the costs.
The Marco e Rosa is particularly worth seeing. It's in a fantastic position, if you can sleep at 3600m. It's also quite expensive, with a grumpy warden.
As I recall the Tschiervahuette was about £27 a night, and the Marco e Rosa about £35, but this info goes back to 2008.
I can't remember if they let you cook your own food at the Tschierva--I think so. I'm pretty sure they don't at the Marco e Rosa.
Sorry not to have more up to date info!