A couple of pointers (based on an engineering approach to the problem):
1. Don't microwave any bagel other than a frozen one (reference my "recipes" post earlier). If it's just a bit stale, toast lightly. Very stale, put it out for the birds! Extremely stale, throw at any squirrel attacking the bird feeder.
2. If bagel is frozen AND a bit stale or freezer-burned, nuke in a bag (paper, rolled up opening) for a time best determined experimentally, taking into account size/weight of the bagel in question and the power of your microwave. My optimum turned out to be 31-32 seconds for a largish bagel HALF. solidly frozen, and this produces excellent results for me 98% of the time. The few failures will have one or two small "extra-chewy" lumps that can be a challenge to consume.
The above also assumes bagels were frozen immediately after being sliced while still warm from the oven! BTW, Max, my wife wanted me to take and post a "selfie" with my classic bagel/cream cheese/onion/lox/tomato Sunday breakfast, but I was too hungry to wait to eat!
On the one occasion I tried microwaving a bagel, it appeared to have been vulcanised. It became unbelievably chewy, nearly resistant to any shearing forces exerted by human teeth. How do you avoid this?