Hello Caroline,
That's a good question. In short, it can be both countable and uncountable. The following definitions might be useful for you.
Hesitation [uncountable, countable] the act of being slow to speak or act because you feel uncertain or nervous
She agreed without any hesitation.
He spoke fluently and without unnecessary hesitations.
Hesitation [uncountable] the fact of being worried about doing something, especially because you are not sure that it is right or appropriate
I have no hesitation in recommending her for the job.
So you can use this word both countably and uncountably. However, it would be unusual to talk about '3 hesitations' for example.
I hope that helps.
Christine