Santa Fe Trailways was the largest member of the National Trailways Bus System when it was formed in 1936. Although Burlington and Santa Fe buses competed with one another on a few routes, their main competition was Greyhound (then partly owned by Union Pacific), so when Burlington suggested to Santa Fe that they form an association, the latter agreed and were quickly joined by Missouri Pacific and other bus lines. The name “Trailways” probably came from Santa Fe Trail, the name Santa Fe used prior to Trailways.
The buses shown on these blotters from Dale Hastin’s collection are American Car & Foundry model 37-P (for 37 passengers), which ACF introduced in 1938. Santa Fe probably didn’t take delivery on these buses until 1939, so these blotters are probably from 1939 or 1940. As noted in this ad, the buses were air conditioned and had comfortable foam seats, but no on-board lavatory.
The Santa Fe Railway sold its interest in the bus company to Continental Trailways in 1948. More Trailways history is available on this site, though be wary of some annoying ads.