Yes, you are eligible for IAS with Hotel Management Degree (BHM), as the basic requirements to apply for the IAS examination is that the applicant should have completed graduation with good academic record and you have BHM degree which is a graduation degree.

You need to appear in the Civil Services Examination, which is conducted by the UPSC. Following are the details of this examination:

Nationality:
A citizen of India, or
A subject of Nepal, or
A subject of Bhutan, or
A Tibetan refugee who came over to India before 1st January, 1962 with the intention of permanently settling in India, or
A person of Indian origin who has migrated from Pakistan, Burma, Sri Lanka, East African countries of Kenya, Uganda, the United Republic of Tanzania, Zambia, Malawi, Zaire, Ethiopia and Vietnam with the intention of permanently settling in India.

Required qualification:
The applicant should hold a degree of any of Universities incorporated by an Act of the Central or State Legislature in India