Living in Arizona, I and others I know hunt not only bull but cow elk in Arizona. Yes, a .30-30 would work, but it depends on where you are hunting. Cover and concealment (for the hunter and hunted) are factors to consider. A lot of the prime elk habitat on the Mogollon Rim and Apache Reservation was burned up a few years ago in the Rodeo-Chedeski fire. 500,000 acres destroyed, and with a perpetual drought, the vegetation really hasn't fully come back yet - I have been helping a student with his Masters in Ecological Restoration/Remote Sensing in this specific area, outside of Heber. There have been other fires throughout the elk habitat of this state that have left large swaths open and without significant canopy cover, and large interspacing (meaning hundreds of meters between significant growths of oaks or shrubs) between plants. The junipers that offered so much concealment are now about 3 - 5 feet tall, and about 2 inches around. The grasses though, because of immediate reseeding efforts, are well-established.
Don't even get me started on what this has done to the mule deer habitat on the Rim and in the Sonoran desert... it's depressing.
My point is that realistically the area that you may be hunting in won't offer you the cover and concealment to do a spot and stalk within the range of a .30-30 (i.e. about 100 yards). It can be kind of hard to hide behind a stand of charcoal. You would be better off with a scoped rifle in .270, 7mm WSM or Rem. Mag (preferably 160 gr. or larger loads), or a .30-06 with 165 gr. or 180 gr. loads. Bullet choice (premium over standard) won't necessarily matter, but shot placement will. So, practice at 200 yards, and be ready for a 300 yard shot if necessary.
I hope this helps.