Australia thought they had dismissed Bell for just three runs before tea on the third day when Steve Smith claimed a catch at gully off Ryan Harris.
But Bell believed there was some doubt as to whether the ball had reached Smith on the full and stood his ground.
The on-field umpires called for the third umpire Tony Hill to adjudicate and he decided there was too much uncertainty to award the catch.
Soon after, a crudely-phrased tweet appeared on CA's official feed, reading: “That decision sucked ass #bull****”.
It was swiftly removed by CA’s media team at Lord’s, and an investigation has been launched. “Apologies for the inappropriate tweet earlier regarding the Bell catch.
It didn't emanate from CA’s official Twitter presence at Lord’s,” read a later message on the account. “CA is currently investigating the matter.”