I don't see how this can be done with a bike that doesn't fold up.
Just looking at the frame alone on my 54cm bike with a tape measurer, it would need a box that is (at a minimum) 39x23 and the rear dropouts are around 6.5" wide (assuming I removed the RD), so 7" to provide some minimal padding. I'm at 69", disregarding room for wheels, fork and handlebars. A 26" MTB frame in Medium/Large size may be a few inches smaller than my 54cm road bike.
I don't think it fits, but would love to see someone prove me wrong.