Not a native Hebrew speaker, but native English. In English, this definitely means that the bear likes some specific honey. If we said "The bear likes honey," it would mean the bear likes honey in general. I don't know for certain if the distinction is exactly the same in Hebrew, but if someone said this sentence to me in Hebrew, as a semi-fluent speaker now, I would hear it as meaning the same as in English, that the bear ate some particular honey and liked it.
It's a bear. It could be a person without the hey (ha) attached to it as Dov is a Hebrew name as is Yona (dove). (I'm learning Hebrew as well, so I can't say there aren't any colloquial ways you can use it, but I don't remember seeing anyone make a reference on any of the skills I've done so far. I know in Yiddish the Hebrew \Yiddish word for pig is used for pig-like humans, but that's the extent of my knowledge. Update: I searched for Hebrew slang of the word, and it said (on two different sites) it is used by gay men to describe large hairy men. Take that as you will.
If you're talking about https://en.wikipedia.org/wiki/Bear_(gay_culture), then apparently yes: https://he.wikipedia.org/wiki/%D7%93%D7%95%D7%91%D7%99%D7%9D_(%D7%9C%D7%94%D7%98%22%D7%91)