Can the Army or my unit confiscate my bike from outside of the barracks?

I would bring this question up with the Provost Marshall immediately. What is the installation policy regarding locking up bikes outdoors? If an old bike is just rusting away with flat tires and has not been attended too, I can see cutting the locks and confiscating it. Even then, there should be some kind of public announcement about the confiscation of bikes on post. Soldiers should be able to get their bikes back as well. The last thing I ever want to hear of is Soldiers unjustly having their personal property confiscated. I ran into a similar problem when I was an enlisted man in the Navy. The petty officer who tried to confiscated my new bike just wanted it for himself.

A Bicycle according to the Motor Vehicle Code is a Vehicle. At least According to U.S. Army Regulations dated 1913 they are classified as a Vehicle. Yes I have a copy. It falls into the same category as trucks cars and horse drawn wagons. Now since it is a Vehicle it is on par with an automobile as a method of transportation. Which means the Army can according to my understanding regulate them in the same manner as an automobile. Which means designated parking and in the old days even an inspection sticker and they are subject to POV inspections because they are a vehicle.
They must be properly stored "parked" like any other Vehicle. IF your bicycle is over a certain value your commander could even possibly require you have Insurance, because it is a vehicle subject to the same rules of the road as an automobile. Post Regulations can require you to wear a bicycle helmet and other safety equipment while on a road that has traffic.
Simply Put for everyday going back and forth to work I would get a cheaper bicycle and send the expensive one home or find somewhere to store it for recreational use. Either that or buy a bicycle rack that mounts to the back of a car. If you don't have a car then ask a buddy who does. Otherwise you are going to have to park your bicycle where ever the Army tells you to. Work with your Command and explain respectfully that you use it to get to work.

It's not stealing when you've been given notice like you described. I would however raise the issue with your unit to see if there can be other alternatives to securing your bike. I knew people in the past that took their bike to their room; so that could be an option.

When I was stationed at Ft Lewis I had a road bike and a mountain bike that I kept in my room. Do you have enough space in your room for the bike?

Where are bikes properly stored? In a bike rack.
Are bikes authorized to be chained to the pole? No
Can leadership remove improperly stored bikes? Yes
Is your bike stored improperly? Yes

Can leadership remove your improperly stored bike?

When a question starts, “Can the Army do xyz...?”, the answer is generally yes.
Store it in your room, and work the proper channels to get another bike rack installed.

Best of luck