Can I get BAH as an Active Reservist without dependents but pay rent?

SPC (Join to see) it is not a matter of simply taking in a lease and poof! Your Mom is your dependent. There is a documented process to make a parent a dependent. This link has a summary and the individual services have their spin on it, links included.

A parent must usually be incapable of caring for themselves with out the SM. Burden of proof will be on your family and whatever medical provider documentation in support is provided. The link is DFAS. DEERS may also have to make a determination. This should be enough to get you started on your research. If your Mom provides care for you as a WTB soldier in your treatment there may also be assistance for that through TRICARE or the VA. https://www.dfas.mil/militarymembers/SecondaryDependency/SDC.html

If you are simply helping out your family, there is no Army incentive or assistance for that. The fact that you are a reserve component soldier further complicates this. Work with your chain of command. The type of orders you are on will set boundaries on this.

The Army does care, but you don't qualify for BAH.

You are not authorized BAH. To get your mother listed as a dependant requires proof that she is for some reason unable to take care of herself, usually mental or physical medical issues that are not resolveable. If you did get her added you would have to the pay two rents or leases as you would no longer be authorized to live in the barracks. Not sure this makes sense for you. I had many friends and Soldiers over the years Adair parents and they did so on their salary while living in the barracks. Thank you for your service. Won’t be easy.