bit by bit

Also, little by little. Gradually, by small degrees, slowly. For example, The squirrels dug up the lawn bit by bit, till we had almost no grass, or Little by little he began to understand what John was getting at. The first term was first recorded in 1849, although bit in the sense of "small amount" is much older; the variant dates from the 1400s. 

See also: bit

The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.