There is no bank account, just the smart contract. It holds the Ether, OMG, or whatever other cryptocurrency you send to it when you buy Unum. There's a function on the contract to return the total reserve in USD, or you can check the actual values of the variables being used. Anything on a smart contract is public.
You're right that relatively few people have the technical skills to query a smart contract, but that relative few is still a LOT of people who can verify the reserves independently. Versus the almost 0 people who can audit Tether.
If you're interested in interacting with the smart contract (or any smart contract), you may want to install Mist. It's non-trivial to get started, I admit, and the tooling around smart contract is incredibly immature, but..man it's cool ;)
https://github.com/ethereum/mist/releases