If you keep either USDs or BTCs at any exchange or "online wallet" ... you're missing the whole point of Bitcoin, because all you have are essentially IOUs from those organizations.
Those IOUs are subject to various "hazards" such as theft, vandalism (destruction of databases), bankruptcy, judgments, gov't seizure, etc.
Unless you have precious metals in your hand or BTCs in the Blockchain with full control of your own private keys ... all you really have are IOUs with various probabilities of redemption