I got mild altitude sickness when I went to Breckenridge, CO from the flatlands of central Arkansas, so you're not alone.

But, I went to Santa Fe last summer and rode my bike and I don't recall any symptoms. In CO, after the first day I was fine. Maybe try not to ride the first day you're there, and don't drink any alcohol. When you take a rest stop on the way (I assume you're driving), get out and walk around and maybe do some jumping jacks to get your heart pumping a little. I think that would have helped me (but I was on a bus for the whole trip).

Karen