"бывать" is a separate verb which generally means "to happen, to occur". In your particular case you may use it but the meaning is different.

Я каждый день на работе ~ I'm at work everyday. (I spend there most of my working hours)
Я каждый день бываю на работе ~ You can find me at work every day (I visit other places or maybe not, but as a rule, can occasionaly spend lots of time elsewhere during the day). Sort of "I show up at work every day", only not as obvious and doesn't IMPLY that you aren't at you workplace very often.