The real reason why Bernard was free to walk around and haxx everything was because he was never fired in the first place.
The board of directors don't really have the power to fire whomever they please. Typically their responsibilities are fairly limited, relating to the hiring and firing of the CEO and broad strategic oversight. I don't know enough company law to state that its impossible for a board to be able to fire other employees as well, but I've certainly never heard of any having that power. It would be very strange, completely undermining the CEO who they hired to make those decisions.
More importantly, even if they could intervene over the head of their CEO - who I presume is Ford, so I suppose you could argue they wanted to undermine him - one single board member sure as fuck can't just use that power as they please. Board decisions need to be made at official board meetings and voted through by a majority.
Of course I realize this is all just nitpicking, but it still annoys me that movies and shows never seem to pay attention to how a business actually functions. Ties into the rest of the organization being completely nonsensical I suppose.
I don't think that's accurate at all with regards to the context in the show. Ford is not the CEO of Delos. His official position is "Park Director". He is in charge of the operations of Westworld. Westworld is owned by Delos Corporation. Hale is an executive director on the board who is here representing the entire board, including the CEO of Delos. So yes, she does have executive power to fire people who are Delos employees, if she is making an official inspection of the park operations on behalf of the entire board.