The problem is that none of the info you list above is private. You have no legal expectation of privacy in any information contained in a govt issued ID such as the driver's license. Social security numbers are govt issued, DBAs are filed with the County, and bank info (really not private, but there's more protection there--but very standard nowadays for landlords to request). To be sure about your state's specific rules, get a consultation with a local attorney. I can tell you as someone who has represented commercial landlords for years, I have never seen a transaction done without getting the info you have listed. The bank info and SS#s are used to check credit worthiness and assets, the DBA is because he has to make sure you are a legitimate entity. If a landlord does not have this info, it makes it hard later if he has to pursue you or unpaid rent. I usually don't authorize my clients to do a lease without obtaining this info.
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This information is pretty typical. As far as your old deposit, you need to find out if the new landlord has it or what has happened to it. If the old landlord kept it, you will need to consult with a lawyer who handles landlord tenant issues.