Source of quote
Bruce read widely and took aphorisms from many different sources, incorporating them into his writings on his own martial arts and philosophy. The idea behind this quote is ancient,1 but this specific wording appears to come from Mao Zedong:
All military laws and military theories which are in the nature of principles are the experience of past wars summed up by people in former days or in our own times. We should seriously study these lessons, paid for in blood, which are a heritage of past wars. That is one point. But there is another. We should put these conclusions to the test of our own experience, assimilating what is useful, rejecting what is useless, and adding what is specifically our own. The latter is very important, for otherwise we cannot direct a war.
Similar quotes in Bruce Lee's writings
Very similar quotes appear in a couple of Lee's works:
Absorb what is useful. - Research your own experience; absorb what is useful, reject what is useless and add what is essentially your own.
This Book is Dedicated to the Free, Creative Martial Artist
Take what is useful and develop from there.
However, Bruce Lee said and wrote many things very similar to this thought, and to some extent it characterises the ideology of Jeet Kune Do. See this quote from the same book (p.24 and worded slightly differently on p.12):
Jeet Kune Do favors formlessness so that it can assume all forms and, since it has no style, Jeet Kune Do fits in with all styles. As a result, Jeet Kune Do uses all ways and is bound by none and, likewise, uses any technique or means which serves its end. In this art, efficiency is anything that scores.
1. The Eudemian Ethics (Book VII, Chapter I), Aristotle