Originally the phrase probably came from how your boss does things with authority because he has power over you. It has since transformed in pop culture to anyone doing anything really well or with high confidence, sort of bragging about it. Best to use it ironically, or you risk sounding like a douchebag, fair warning.
"I finished that eight page paper for my history class in twelve hours, like a BOSS."
And you have to put emphasis on it, and say it kind of like "bowse!" (or "baus!" to be more phonetic about it).
This music video from Andy Samberg/The Lonely Island humourous mixes this new meaning with workplace situations from its original context [NSFW]:
http://youtu.be/NisCkxU544c
Just for a bit of pop culture.
But no, you wouldn't use it anymore to refer to something your actual boss does, and if you did it could be considered as making fun of him/her. Nor does it mean that you are being controlling, like Richard's example 2. That would be better said as "She thought he was being bossy." Saying "He's acting like a boss" sounds like he's in a play or other theatrical production and his acting is really good.
Tricky because it's a really American colloquialism that popped up recently. Hope this helps! :-)
Dan