I wouldn't recommend rubber banding the tail. Just keep the area clean. If it is severed completely, it will fall off on its own. My Water Dragon just pinched the tip of his tail recently. Took a couple weeks but the tip did fall off. We soaked it in betadine twice a day for about 5 minutes and swabbed it with neosporin 2-3x a day. He was also put on antibiotics by the vet to prevent infection so this may be something to look into.
Look, I know separation is a huge debate on this forum. Some people do house beardies successfully. I even used to do it provided they were a similar size. But I realized after a year of caring for them, there is always the 'smaller' one, the one who doesn't get access to a good basking spot or who chooses not to eat in front of the dominant one. Beardies make a hierarchy when caged together; there will always be the prince and the pauper. To prevent them from suffering any more than they have to, separation is ideal. My dragons are permitted to play together every few days because my male gets lonely. I do not let them spend the night together unless I am breeding. Otherwise, everyone has their own tank and setups, their own lights, their own food dishes, etc. It's just better that way.