I don’t really know anything about Nestor Makhno’s portrayal in Soviet history books, but I can provide an answer regarding contemporary Bolshevik opinions of Makhno and anarchism in general, which will hopefully satisfy at least part of your question. To start, here is an excerpt from Demanding the Impossible by Peter Marshall:

When he visited Moscow in June 1918, Lenin received him at the Kremlin. The Bolshevik leader complained of the ‘empty fanaticism’ of most anarchists, and he declared to Makhno ‘if only one-third of the anarchists-communists were like you, we Communists would be ready, under certain conditions, to join with them in working towards a free organization of producers.’ (Marshall, 473)

So, right away we can see that Lenin holds anarchist-communism in contempt. At the beginning of the Russian Revolution, anarchists and communists were working together, with four anarchists even holding seats on the Military-Revolutionary Committee. It didn’t take long for the Bolsheviks to turn on anarchism however; within a few months the Red Guards and the Cheka were arresting hundreds of anarchists in Moscow. Lenin called them “armed detachments of counter-revolutionary burglars and robbers which had taken refuge under the black flag of anarchy” (Marshall, 473).

On route to the Ukraine, the Bolsheviks proposed to Makhno that he should select a certain region of the Ukraine and carry out secret revolutionary work there in their name. Naturally he refused even to discuss this offer; the tasks he had set himself had nothing in common with those of the Bolsheviks.

The above quote is from Peter Arshinov’s History of the Makhnovist Movement (1918-1921) and discusses Makhno’s return to Ukraine after his meeting with Lenin that I quoted earlier.

The Bolshevik Brest-Litovsk treaty granted Ukrainian lands to Imperial Germany and Austria, who in turn re-established the power of the aristocracy and gentry. The Ukrainians had just fought these people in the earlier October Revolution, and now they had to do it all over again. Makhno and his Black Army rose to prominence in the fighting that followed, and it was this second outburst of revolutionary activity that led many of the peasants in southern Ukraine to eventually take up the black flag of anarchy. Suffice to say, none of these people were fans of the Bolsheviks.

I’m going way more in-depth than probably necessary, but it’s kinda hard to contain yourself when discussing something so personally interesting. Like you said in the wording of your question, one of the many enemies faced by Makhno and his Black Army was the Red Army of the Bolsheviks. It would be this army that eventually defeated Makhno. The Makhnovischna and the Bolsheviks had made two military alliance/peace agreements while both were fighting against the common enemies of the Central Powers, the Russian Monarchists, and the Ukrainian Nationalists. After the Makhnovists had defeated the White Army under General Wrangel, the Bolsheviks sent an ultimatum demanding that Makhno and his troops be absorbed into the ranks of the Red Army. The Makhnovists refused. The Bolsheviks responded by arresting and executing much of Makhno’s staff during a joint military conference. Makhno continued to fight against hopeless odds for several more months, until the severity of his wounds caused him to leave Ukraine for medical treatment. The Bolsheviks declared him to be a bandit and a pogramist, and he was forced to live the rest of his life in exile. Makhno lost a lot of comrades and friends in the war against the Red Army, and he would continue to be outspoken against the Bolsheviks until his death.

Much more could be said about the battle between Makhno’s anarchists and the Bolsheviks, but the gist of the matter is that the Bolsheviks were more interested in creating a “dictatorship of the proletariat” under one party than they were in cooperating with fellow leftist groups. I would recommend reading through this archive of Makhno’s writings to get a better idea of his views on Bolshevism and the conflicts the philosophy had with his own anarchist thinkings. Arshinov’s History of the Makhnovist Movement (1918-1921) has a clear bias towards the Makhnovists, but it is an interesting fairly contemporary source that quotes several primary documents within the text.

Sorry for the long-winded answer, but hopefully I was able to show that the Bolsheviks and the Makhnovists viewed each other in a negative light almost from the get-go. If Makhno did have a place in Soviet history books, it would have been as a counter-revolutionary and an enemy of the Party and the State.