Exhibit 23.2

Consent of Independent Registered Public Accounting Firm

We consent to the use in this Registration Statement on Form S-1 of bluebird bio, Inc. of our report dated March 21, 2013, relating to our audit of the consolidated financial statements, appearing in the Prospectus, which is part of this Registration Statement.

We also consent to the reference to our firm under the captions “Experts” in such Prospectus.

/s/ McGladrey LLP

Boston, Massachusetts

May 14, 2013