Was Bose right or left-wing? I'm not sure the distinction is that relevant. The lines between right-wing and left-wing extremists can get hazy, especially when national independence is the main goal motivating them. Bose was a revolutionary action-oriented nationalist who disliked liberal democracies and would turn to anyone who seemed likely to support national liberation.
His association with Berlin and Tokyo makes people label him "right-wing" but there's a lot of uncertainty and guesswork involved in such a description. Bose was never attracted by Hitler's racial views and didn't feel at ease in Berlin. He literally made his way to Berlin through Moscow, and perhaps figuratively as well.
Bose was a nationalist and a libertarian, he was repulsed by the very notion of a welfare "socialistic" state that Nehru had in mind.
But he wasnt right wing or even related to any HINDU fundamentalist group either. The people who assassinated Gandhi were Hindu fanatics who were religiously insular. They had NO contact with Bose or vice versa, infact, Bose would've gone after them first if he had come to power. Afterall, some of his most trusted aides were muslims.
Bose, was a super intelligent person (educated in UK, he topped the British civil services exam) known to be very charismatic and charming.. he envisoned a secular and capitalistic state out of India, which he thought could only be realized by a violent revolution agains the brits, not by the non-violent, pacifistic means that Gandhi was envisoning and the socialistic welfare economy that Nehru was proposing.. he was very much against these two notions, and thats why he left the Indian National Congress.
He was an undeniable patriot, whose legacy is now exploited by the left, right and centre to their own benefit, and some Indian liberals are defiling it just for the sake of media attention..
Then we can call Bose the Indian Eamon de Valera.