Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in Registration Statement No. 333-185073 on Form S-8 of BSB Bancorp, Inc. and Subsidiaries of our report dated March 15, 2019 relating to the consolidated financial statements and the effectiveness of internal control over financial reporting of BSB Bancorp, Inc. and Subsidiaries appearing in this Annual Report on Form 10-K of BSB Bancorp, Inc. and Subsidiaries for the year ended December 31, 2018.

/s/ Baker Newman & Noyes LLC

Boston, Massachusetts

March 15, 2019