"He (Shah) asked me to give good governance in the state. I assured him that whatever faith you have reposed in me, I will do," the newly-appointed chief minister told PTI after meeting the home minister here.
Bommai is on his first visit to Delhi after becoming chief minister. He is scheduled to meet Prime Minister Narendra Modi at his residence later in the day.
Apart from Shah, the BJP leader also met Defence Minister Rajnath Singh, Parliamentary Affairs Minister Prahlad Joshi and Jal Shakti Minister Gajendra Singh Shekhawat.
Bommai, who was elected as the new leader of the BJP legislature party in Karnataka on Tuesday following B S Yediyurappa's resignation, took oath as the chief minister on Wednesday.