I am not sure how much of the New Mexico section of the GDMBR overlaps with the CDT, but in poking around about riding the CDT (as per recent efforts posted in this forum!) I discovered this great document about water caches along the CDT. Very helpful info created primarily for thru hikers, but still relevant. I have ridden a good deal out in the Chain of Craters area as well as further north in the Zuni mountains. In all my time out there (day rides and bikepacking) I have never found a reliable water source. Tanks, reservoirs, springs, etc. are notoriously inconsistent, non-functional or just dry because of lack of precip. Don't rely on the maps.
The NM CDT water cache file:
http://www.blm.gov/pgdata/etc/medialib/blm/nm/programs/recreation/rec_docs/cdt_maps.Par.28024.File.dat/Stash%20box%20locations.pdf