Ich arbeite bei Berlitz. When you used arbeiten für that means you are working for a purpose. Für etwas einsetzen. When you used arbeiten bei means that you are working for a company. Arbeiten bei einer firma. Example arbeiten für eine politische Idee, arbeiten bei GmBH. Hope it helps! 

Is Berlitz the name of a city or is it the name of your company?

Ich arbeite für Berlitz

implies that your work FOR something or someone so I would think then it is the name of your company or of your boss.

Ich arbeite bei Berlitz

could mean both. If Berlitz is a city it would mean that your working place is NEARBY Berlitz. If it is a company it could mean that you work FOR them.

Ich arbeite in Berlitz

is the way to make clear that you emphasize the location.

Perfekt! This cleared things up !