Online Banking: What’s a good way to programmatically create virtual savings “buckets” for users?

I doubt any US bank would allow you to do a carte-blanche user sign-up via an API. What they will do (considering you have a strong business case and they want your business), is that if you're numbers are good enough, they will designate you within their Banking software as a virtual branch, and within the branch, you can then sign-up as many accounts you want. However, the entire entity would be treated as a singular account. Though you will be able to distinguish between the sub-accounts and move money amongst them, the bank will see you as a singular entity. Since this would most likely be a commercial arrangement, it is questionable that this would be protected under FDIC (Checking/Savings) program.

This would have to be a specialized arrangement with the bank and the bank (depending on how they are setup) provide you with a Web Services or an API.

There is nothing like this (to the best of my knowledge) that any bank is offering as a standard, off-the-shelve product offering.