Well, when I was a trucker, I hauled many loads of bagels from various suppliers to end users . They were always frozen when picked up and delivered . Based on that and personal use, they may be frozen prior to toasting ; but once toasted or grilled, etc. not so good if frozen and re- heated.
Freezing bagels is a good way to retard mold growth. However, you sacrifice moistness as it escapes from the bagels within the bag. You could mitigate this by placing them in a double wrap plastic bag, but you'll still have it.