(rhetorical question) Just what part of this mans' Army are you in?? In the 1960s, in the Army Security Agency I was the only cyclist on base and could leave my bike unlocked anywhere on base. Consult with the MPs and your senior Sergeant for ideas.
Ok for the cheapo bike idea. My army bike was a three speed. Cycling paid off for me in the Army. In our one annual physical fitness test I lapped every other soldier taking the mile run test on a 1/3 mile track.