push bike do not need paper work in the USA or Mexico that I know of.
But a motorcycle will and I think that is what you want to know.
I posted in a few treads how.
but to cut it short you pay for the bike get signed title take that in to a title office in town and get new title in your name with registration and new plate for the bike and then get insurance even if your gust riding it 20 feet in the USA you need it by law. You are good to the border then. Better have a motorcycle licence for it.
When are you going better be soon it can get cold even down there.