This has been an interesting little discussion. I've tried to remember the bridge, as I drove by it many times on trips from Chama to Denver. Had no real luck with that.
I would guess that it is a plate girder bridge, supported by reinforced concrete piers. I find it difficult to believe that a wood trestle would be used here (except in the very early days). Keep in mind that the area drained by the Rio Grande above Alamosa is IMMENSE. Springtime runoff flows would be very heavy in some years, and carry a lot of debris. It just doesn't seem like a good place to have a bunch of pilings in the river.