The last minibike I shipped I used two 36" x 24" x 12" double-wall heavy duty boxes from Home Depot. They were like $15 each and I put the two together to make one custom sized box that ended up being around 36" x 24" x 18" and packed it up nice with Styrofoam peanuts, bubble wrap, and used paper wrap, and cardboard and anything else I had laying around that could be used as packing material and taped it all up good. I shipped it Fed Ex Ground for like $70.
I also have bought complete minibikes and had them shipped. One was a Ruttman long frame I bought from a guy on this forum. He shipped it from Michigan fully assembled except for the front forks and handle bars which were unbolted and positioned in the box to fit. Everything arrived in perfect condition.