I would say all the MBBs have pretty strong entrepreneurial ties, not just Bain. Quite a few tech CEOs / executives are ex-McK (Sundar from Google, Sheryl from Facebook).
I work at Uber currently and it is true that a few of the top Operations executives are ex-Bain. Bain also has very strong roots in private equity of course.
I worked at BCG and a little known startup fact that I am proud of - Clayton Christensen, who developed the theory of Innovator's Dilemma, is ex-BCG.