As a nonresident you're still allowed to drive here. Depending on what bus you choose and how in-depth of a conversion you want to do, it may take a little longer than a month. Many of us have several years into our conversions. It's good if you find a place where you can, without question, park you bus during your build process.
You don't need a special license to drive a privately owned bus. License is required if used for business.
Technically it's probably best if you don't tell any officials about your plans to live in a bus. Don't lie, especially at the DMV, but don't offer unsolicited information. Don't mention conversion to motorhome. Just register it as a private vehicle if possible. Mine is registered as a van. If you eventually convert it to a motorhome, then register it as such the next time you have to re-register. When you get closer to having a bus ask someone for specific information on how to get insurance without so much hassle.
I think you can do it. Good luck.