Now, saying that were-bears will be in Dragonborn, Aaaand saying that we will have the ability to become one... My question is this:
In order to become a were-bear, (and we're already were-wolves) will we have to cure ourselves of were-wolf lycanthropy first?
EDIT::::
Second question: Will the Ring of Hircine effect Were-bear Lycanthropy too?
Question one, yes, you cannot be two different werecreatures at the same time. Case in point with the uncontrolled type (assuming they didn't already retcon them out of the lore as I predict they will

), what would you transform into on nights when one or both moons are full? With the Companions type, well, it might be possible, but it sounds kind of messy (and crowded) if you ask me. It wouldn't surprise me if it could cause one's body to explode from overload or something (you'd understand what I'm talking about if you've played through the Companions questline).
Second question, I have no idea, I guess it would affect werebears as well.
One final note, yes, werebears WILL almost no doubt be another quest-related ritual thing just like werewolves in Skyrim and the Vampire Lord when/if they do them. They are never doing lunar transformations again as it apparently violates modern acceptable game design (at least in Bethesda's opinion), and they are likely never doing lycanthropy as a contagious disease again, although Bethesda's known to change their minds on stuff and what is "acceptable" in their eyes.
Spoiler I actually don't think lunar transformations would be a bad thing if it's attached to a quest which can allow full control over transformations as the reward. Could be an interesting idea for a future title, actually.