I thought it would reflect badly on me so I tried to hush the whole thing up.

我想此事会给我的公众形象造成很坏的影响，于是我想方设法不把它声张出去。

《柯林斯英汉双解大词典》

I suppose Dumbledore is trying to hush it all up.

我想一定是被邓不利多压下来。

youdao

Hamilton says he failed tests, but managed to explain it away, or hush it up.

BBC: Lance Armstrong: Tyler Hamilton on 'how US Postal cheated'

They often receive threats to hush up the capture of drug suspects because it makes the cartels look weak.

FORBES: More Journalists Killed in Mexico’s Drug War than in Afghanistan