I make homemade bagels occasionally and usually freeze the ones we dont eat immediately.
I have more experience with Fresh bagels from the Bagel store.
I make it a point to get too the boatel store as soon as they open, to assure me that Im getting Bagels that are still warm out of the oven. The longer they sit out, the less fresh they are. I personally dont like toasting my bagels, so I have a small window to eat them in their freshest state. Even after freezing them, in my opinion, unless they are toasted, they're not that great.
I find toasted fresh bagels and toasted fresh bagels that were frozen to be very similar in quality. But even if a fresh bagel is immediately placed in a sealed plastic bag and kept at room temperature, it still looses something ( also, putting it in the bag too early after cooking may make it get soggy).
to sum up my experience
Fresh out of the oven is best
Fresh frozen, and then toasted is second best
Older frozen then toasted is ok
Sitting in a bag at room temp for a few days is ehh at best.
Call me a bagel snob lol, I've lived in NY most my life so I'm used to decent bagels.
***As a side note, Ive had mixed results with homemade bagels. The taste is there, even the consistency is pretty good but they dont always rise as well as the recipe says or shows that it does. Ive used the correct / freshly bought flour and tried multiple recipes. Probably a 'me ' thing, but ive been pretty consistent screwing it up.