Nepal, like other places in Asia such as Bhutan, was never directly colonised. However, certain areas, such as diplomatic relations, were controlled by the British.
There are a number of factors which induce a European empire to colonise an area. Firstly, it has to be economically viable. India is a much more economically sound area to colonise than Nepal because while India has a multitude of resources, Nepal does not. It also has to provide the colonisers with money, depending on what they put in. While many of the colonies were not economically viable in the long run, there were still natural resources and other items that the colonisers would be able to extract. Nepal, for the most part, did not meet these requirements although it became a market for the products of British India.
Secondly, it has to be accessible. Nepal is flanked by India and Tibet. The British, while controlling India did not have the manpower needed to control Tibet and more importantly it was hilly, mountainous terrain that is not easily controllable. Thus the only place where there is a reliable access route is through India which the British did control. Having a firm control there was not needed when the only market readily available was British India and that you could get the Monarchy of Nepal to do your bidding without too much of a bother.
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Related question: I've read Nepali prime minister, (or king I don't remember) after India's Independence when Princely States were joining India, wanted to join India. But Indian PM Nehru refused. Why Nepal wanted to merge with India and why did Nehru did not want that?
Related question, why were polities like Nepal and Bhutan never fully incorporated into India in spite of, effectively, being princely states?