Defender Shorey showed Reading's strikers the way to goal as his first ever senior strike decided a one-sided game.
The left-back finally made the breakthrough for the home side 20 minutes from time with a neat finish at the second attempt.
Shorey, without a goal in his 66 previous games for Reading and Leyton Orient, saw aright-foot shot blocked, but made no mistake at the second attempt with his favouredleft boot.
The goal was a huge relief for the home side who had dominated through out, but hadwasted a string of chances.
Striker Nicky Forster was the chief culprit. With four goals in his previous three games, thestriker was presented with no fewer than nine chances but failed to tuck any of themaway.
Forster could have scored a first-half hat-trick, but saw shots fly wide of either post andwas also off target with a free header from a Shorey cross after just seven minutes.
Despite Reading's dominance, their only first-half effort on target was a header fromdefender Adie Williams, which goalkeeper Steve Banks did well to claw from under hiscrossbar.
And Banks looked like emerging as the Bradford hero when he saved a Forster penalty on57 minutes.
Stephen Warnock pulled down Forster in the penalty area, but the striker still could notfind a way through to goal as he saw his low spot-kick well stopped by the alert Bantamskeeper.
But Shorey finally made the breakthrough after 71 minutes when he drove through acrowded area with a neat finish at the second attempt.
The visitors, who were confident on the back of their impressive win against high flyingNorwich on Saturday, had few chances against the lively Royals but midfielder Paul Reid,who struck twice on his first start at the weekend, forced Reading's goalkeeper, MarcusHahnemann, into a smart low save.
The American keeper was also at his impressive best to beat out a second-half snap-shotby the otherwise redundant Danny Cadamarteri