The seamer (58) starred with the bat rather than ball on Thursday as he and last man Mohammed Shami (51 not out) put on a record partnership for the 10th wicket of 111 to help the tourists to 457.
It was a second successive day of toil in the field for England in Nottingham but, when India took to the field, they were able to remove under-pressure Alastair Cook before England reached the close on 43-1.
Bhuvneshwar is confident they can continue to make further progress on day three, and expects the Indian spinners to come into play as the game goes on.
"It was a good day because it's not a good wicket for bowling so we needed at least 450 runs," said Kumar. "Now it's time to bowl really well.
"We are confident we can get them (England) out. The pitch might help the spinners later on."
Sam Robson (20 not out) and Gary Ballance (15 not out) will return on Friday with England 414 runs behind.