What regulation addresses soldiers' rights when inspecting gear/bags for stolen items?

I do not know, however 1SG, if this is a time sensitive question... the best recommendation would be to contain all personnel with bags/gear and contact the MP's immediately. They can either advise you, or come conduct the search. If you are tying to keep it more "in house", you could put it out that punishment would be less severe if the perpetrator comes forward during an "amnesty period" but if not and the MP's get involved, you wont have any choice but to crush them (obviously in more tactful and professional wording haha).

manual for courts martial section 3. Rule 314 specifically identifies searches not requiring probable cause. otherwise you will still need a search warrant.

1SG, 735-5 (Property Accountability Policies) May help, or be a good starting point. It has sections on OCIE layouts in it. Not sure if the exact situation you are trying to research, but I hope this may help.