Do I need EPA registration to sell a private label bathroom cleaner?

Only if your product makes pesticidal claims — for example, 'kills 99.9% of bacteria.' General-purpose cleaners without kill-claim language are not EPA-registered products under FIFRA. Many co-packers hold existing EPA registrations you can private-label under for a licensing fee. Confirm this in your first conversation with any manufacturer you find through AJ Cosmo Labs or elsewhere.