That is false. While Inazō Nitobe’s Bushido: The Soul of Japan (1899) popularized the term in the West and reframed it as a moral philosophy, the word bushidō itself long predates him. It appears, for instance, in the Kōyō Gunkan (c. 1616) and in writings by Yamaga Sokō and Daidōji Yūzan, where it already referred to the “proper way or path of the warrior”. So, it can be said that Edo-period samurai were familiar with both the term and the ethical ideals it denoted…though I can concede that its meaning evolved over time. However, Nitobe certainly did not invent the concept bushidō; he reinterpreted an existing Japanese concept for a Western audience within a Meiji-era, Christian-humanist framework.
Meanwhile, the groundwork for the formation of the concept of bushidō was done in Kamakura and Muromachi periods, its ethical substance was codified under terms like kyūba no michi and shidō, and is well-attested to in period texts and chronicles eg. Heike Monogatari (平家物語, early 13th c.), Taiheiki (太平記, 14th c.), Chikubashō (竹馬抄, 1383) etc.