In Chekov's play, The Bear, the stage direction notes that Smirnov is jabbering (talking endlessly on) and Popova is trying to get his attention by repeating "Bear! Bear! Bear!. And though that may well have been Chekov's initial intent, I would think more meaning would come from the actress's choice as to how to play the role. Since they are fighting back and forth, I would think she could be calling him "Bear" repeatedly as a taunt, the way children do—for there is no doubt that these adults are being childish.
Popova's insults begin with:
You're a boor! A coarse bear! A Bourbon! A monster!
When he asks her to repeat herself, amazed that she has insulted him, she says...
I said you are a bear, a monster!
He is so enraged by the time that she starts repeating "Bear!," that he figures a woman cannot get away with insults any more than a man, and so he challenges Popova to a duel. Amusingly, she accepts, though what is even funnier is that Smirnov must instruct her with regard to firing a pistol in the first place.
Remember that this was written as a satire—something that makes fun of a person, place, event, idea, etc. In this case, Chekov was said to be making fun of...
...liberal discourses in mid-to late-nineteenth-century Russia, in particular those concerned with "The Woman Question."
The "Woman Question" refers to the emancipation of women. Smirnov refers to this when he considers that in light of Popova's insults, she must be one of these liberal women:
It's about time we got rid of the prejudice that only men need pay for their insults. Devil take it, if you want equality of rights you can have it. We're going to fight it out!
In that Smirnov acts like a bear, with (as Popova says)...
...large fists and a bull's throat...
...I would suggest that Chekov may be expressing humor over the noise being made about equality for women. If the play is any indicator, it would seem that perhaps men complain about women being emancipated, while ironically, they find these kind of women infinitely more attractive than the simpering and manipulative ladies who don't come out and tell a man what they want, but trick him into getting their heart's desire.
"Bear" may be symbolic simply for the lumbering clumsy animal that makes a great deal of noise, but is essentially interested in eating and sleeping unless he is angered. When Smirnov arrives, so frustrated and angry about his finances, he certainly seems to act like a bear.