When I lived in Phoenix (and the gym in the building that let me use their shower closed), I had to change a few things to still allow the commute possible. Shower in the morning before the ride. This works in every climate, but especially in Phoenix. Clean bodies don't have the bacteria that allows B.O. to form. Also take food/clothes/clean up kit to work a couple days in advance, this way you don't have to carry anything on your back. If need be, use a bus/light rail "boost" to shorten up the morning ride. Take your sweet time and don't overdo it. Use the last mile or two to cruise and cool down. Then when you get to work, freshen up in the sink and change clothes.

You can also see if there's a gym nearby work that will let you get a shower only pass.