"Mini Bike" is the "correct' answer as far as initial use and coining the phrase.
From the Taco/Steens site, and referenced here in OldMiniBikes before:
"In March 1960 Rod and Custom’s new product section “Auto Mart” highlighted the Viper Cycle. This might be the first time the name Mini Bike is used to describe this new hobby in print."
Note that R&C's Editor Lynn Wineland was heavily involved in "mini bikes" after they became popular enough to grace the magazine.
Note that Charles' magazine was dated in November of that year, so while Wineland used the term "mini bike," the hyphen on the cover could have been artistic license, but it wasn't the first time the term was used. Anyone got something earlier than March 1960?
The first "mini bike" on the "mini bike" craze, not including scooters, or paratrooper two wheeled bikes, or anything Leonardo Divinici built out of oak was the Bug Flea. It beat the Go Kart Mini Cycle out the door by a week. This was in 1958 when both the Go Kart Co. and Bug Engineering had been neighboring competitors with the race karts.
I've also heard the Ruttman/Michrina theories. Neither built bikes before 1958, (1959 Michrina) and Ruttman's earlier bike was referred to as a scooter. But that is a discussion for "first mini bike" not first use of the term, nor correct spelling.
From a purely phonetic aspect, it would have been two words, etymology and all that. It's never been one word, but you have to use it when searching for sales on line of course.