I've heard this expression a couple of times before. It seems related to the engines, but I can't find any information on it, except in the context of testing them.
Here's two videos where it occurs: Atlantis launch, Columbia launch.
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The space shuttle throttled down its main engines from the normal setting of approximately 104% to around 67% as it was passing through the region of max dynamic pressure ("max q"), to make sure that the certified dynamic pressure limit was not exceeded. Once the threat had passed, the engines throttled back up. If you plotted throttle level vs time on a graph, the throttle down region looks a bit like a bucket, hence the term.
See my answer to this question for some specific numbers from a particular flight.
Edit: a graph showing the "bucket", from here.
answered Jul 4, 2016 at 0:25
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$\begingroup$ I think the thrust bucket also kept the g-loading down below the STS system's limits too. $\endgroup$– ErikJul 4, 2016 at 5:38
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1$\begingroup$ One should remember the SSME provides around 2,300kN each (x3). Meanwhile, SRBs are contributing 12,000kN each (x2). So throttling the SSME to 67% is in fact less than 10% thrust drop; and considering a considerable amount of fuel is depleted, TWR (and acceleration) are considerably higher than at launch. $\endgroup$– SF.Jul 4, 2016 at 7:16
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6$\begingroup$ The STS SRB grains were shaped to provide a thrust decrease during the max q region as well. $\endgroup$ Jul 4, 2016 at 12:00
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2$\begingroup$ "the normal setting of approximately 104%" lol $\endgroup$ Jul 4, 2016 at 14:04
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1$\begingroup$ IIRC 100% is 100% of the performace for the original engine. They since improved but the old trust max is still referred to as 100% $\endgroup$– HennesJul 4, 2016 at 16:42