Following consultation with the Rugby Football Union and the England and Wales Cricket Board the FA hope to have its players on board before next month's friendly against Sweden.
"The England players are representing their country, they're role models, their behaviour is incredibly important in respect of everything else we're trying to do," said Bernstein, speaking at the opening of the national training complex in Staffordshire, central England.
"I feel very strongly about that. It should really have been brought in years and years ago. Clearly in the past we have been hampered by not having a code and some things have been less clear than they might have been."
The FA charged Chelsea's Ashley Cole with misconduct on Monday following the defender's offensive tweet after the governing body's independent commission had queried what they described as his "evolving" evidence in the John Terry racial abuse verdict.
Chelsea team-mate Terry, who retired from international duty last month before being found guilty by the FA of racially insulting Queens Park Rangers defender Anton Ferdinand in October 2011, was twice stripped of the England captaincy for off-field distractions.
The code, which has been in planning stages for some time, was not a reaction to the Cole or Terry sagas and has three sections.
The first refers to general conduct, whether a player is with England or not. The second concerns players' conduct when on England duty and the third, how the FA will manage the process of breach or alleged breach.
The code also concerns social media use, especially players' use of Twitter to air their views.
"We've explained to the players that that's absolutely fine by us, but please understand if you're using Twitter when you're with the team you should do so in conjunction with the team's media officers," said Club England managing director Adrian Bevington.
"When you're not with the team, clearly you should avoid any criticism of any organisations or individuals."
Cole approached Bernstein to apologise in person for his Twitter insult aimed at the FA.
"He was very contrite and emphasised that what he'd done was in the heat of the moment. He had publicly apologised and withdrawn the tweet as quickly as he could," said the chairman.
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