If my bank ever started asking questions about NETeller, or about where I was getting the money, I would switch banks immediately. You want my business? Then mind your own business. There are plenty of banks out there that would be happy to have me as a client without giving me the third degree about my personal business.
That said, I do think it is smart to keep the transfers under $10k. If you transfer more than that, the bank has to file paperwork and report that deposit to the IRS (I think).
If you’re looking for a new bank, there are many “online” banks you can choose from. You aren’t necessarily limited to the local banks in your town.