Return bags with no tag on.

Hmmm, not sure. I'm thinking since it's a dept store, all tags must be attached for a return. But if you found something wrong with it, they should be able to take it back. Maybe talk to your SA before you go?
 
I'm not sure about Bloomingdales, but I have seen Chanel bags without tags attached at NM, saks, and even the Chanel boutiques. I'd talk to your SA and explain the situation.
 
dunno because the Chanels I bought already had the tag cut off in the first place. The tag(s) were unattached, inside the purse.

I thought they might have been returns, too, but I wasn't worried about it because the purses didn't look bad.

Maybe you should call Bloomingdales, or specifically, the Chanel dept. and ask them
 
Should not be a problem. I never shop at Bloomingdales but and SA once told me their policy is to accept any return as long as you have the receipt.

As a side note you can buy the little plastic tag fasteners at the office supply store, they are cheap too less then $2 for 50. They come in handy when you need to remove the tag on something to try it on, like a belt.