If you know your history
Then you would know where you coming from
Then you wouldn't have to ask me
"Who the heck do I think I am?"
-- Bob Marley
It seems to me that would be one of the harder groups to get within. While there has been some acceptance (and not without some friction) within the gay/boi/leather/S&M/bootblack deal, the whole bear culture which is less focused on actions and roles, but more on just plain old body-type, Big, Hairy, and Big, did I say Big? Like huge/fat/beer belly - guys with the hots for Santa Claus. It also is much more physical, with lots of physical contact and lots and lots and lots of nudity (where the leather deal is far more costume/role focused).
A classic bear event would be a camping trip where all the guys were hanging out looking like Larry the Cable guy, with pretty much his mannerisms and manners too.
It's pretty much the direct opposite to the more classic thin/hairless/very young and boy looking/nelly/effeminate gay stereotype. It's basically guys who like other guys for just being guys. Guys who are really hot for beer-drinking, public pissing, redneck guys who love nothing more than being out in the woods camping on a hunting trip. They tend to the more rowdy, uncouth (as opposed again to the more classic Judy Garland and Opera gay guy acting like Carry Grant stereotype), rough-housing, 'rasselin', boxing, big assed-motorcycles and pick-up trucks image. They ain't listening to opera or show tunes, they'd take a shotgun to any boom-box playing disco/electronics/dance. They play hard core county and metal. Rob Halford/Judas Priest/Metallica type classic metal when the Hank Williams and Willie Nelson classic country ain't on.
Pretty early on in the entire gay deal (early/mid 60s) the first gay motorcycle clubs the Warlocks and the Satyrs1 (all what would come to be called 'bears' no such term existed at that time) and the Hell's Angels bonded over big bikes, overindulgence in alcohol and love of lewd, licivious and gross behavior and a very tight personal bond between Sonny Barger (the founder of the Angel's) and the founder of the Warlocks, as well as what was often a shared military background. As a result the HAs have never been a threat to the gay community (in the way that they really went after the anti-war/anti-draft people for a long time), and in fact have helped out security wise at several prominent gay-community events including the funeral of Gwen Araujo. Something many of our TG fellow sisters and brothers would not do out of fear of being seen with other TG people.
The chief problem with a FTM being a bear assuming they were physically big enough would be the nudity deal and the how many things can I do with my cock deal. It's very cock centered.
1 - Founded in 1954 in LA by the way, Warlocks in 1960 in SF.