I think it’s safe to say that bear, used to describe a man, has gone down the same road as gay. For instance, all the Dopers who have bear in their names, I assume are gay men.
To hell with the children! The Gays™ are trying to take our vocabulary!
There are plenty of people who work at the pentagon who are contractors - my partner nearly got sent there for a few months. I’ve never met a soul, nor heard of one either, who had a rainbow sticker on their car who wasn’t gay, or borrowing the car!
“Bear” has meant hairy gay man around here for at least 15 years, if not more. (Bit of a problem when I call my partner “Bear” (a nickname she earned about 18 years ago!) in a gay environment.
Gigi, being a gay bear really isn’t as much a sexual thing as much as it is a social and cultural thing. Gay bears are a gay subculture. There is no need to feel uneasy about it. It sounds like the man is simply trying to bond a bit and wants you to get to know a little bit about him.
As for the rest of you, I’m surprised the nobody has said “Woof” yet…lol. 
Gigi, as others have mentioned being a bear has nothing to do with sexual roles. A bear can be a top or a bottom or both or neither, and your coworker has not revealed anything inappropiate to you. And a bear is not necessarily “butch,” either; I’ve known some very sweet, soft-spoken bears over the years. Also . . . I’ve been familiar with bear culture for a few decades now, and it always refers to gay men. A straight guy can be, physically, a bear, but AFAIK there’s no straight bear culture.
FYI, Bear_Nenno is not. He’s married to a lovely young woman. But I think the rest of them are.
That’s hot.
Or at the very least, someone who wouldn’t be offended if you assumed they were gay.
Are you going to tell us that, “I want a pic-a-nic basket!”, is a reference to some sort of gay sex act?
Wouldn’t you be more surprised if we told you it wasn’t?
I don’t think there is a phrase or word that a post-adolescent male can’t turn into a sexual phrase. It’s a skill we all share gay or straight.
20 years ago, it denoted “cop”. Sometimes still does (IIRC, Bear_Nenno is in law enforcement).
Wait 'til you hear my predictions for the Packerth/ Cowboyth game. The first quarter drive will be spectacular… and did someone say, cheesehead, oooo honey! In the end, I think they’ll cover the spread, but I hope they don’t. 
This is what I was thinking of, too (a Zuni bear). Bears are very common Native American totem animals. I think that in some areas of the country you would be way off base to assume any guy wearing a bear emblem (as clothing, jewelry, or tattoo) was necessarily gay. And as for bear claw emblems, they’re common as dirt in the town I went to university in, with its bear mascot, and many people there would not only disagree but take active offense at the idea that having those emblems on their cars amounts to some declaration regarding sexuality.
So I think it’s a matter of context. “Bear” does mean “big gay guy” in a certain context, but in many other contexts, it doesn’t. And I understand gigi’s minor issue with her coworker, who IMO was trying to act as if his context was the universal one and as if gigi was prudish or stupid for not knowing that. A stylized bear on a coffee mug is not “a gay thing.” It’s a freaking coffee mug.