What is Titty Bear?
1.
A name you'd call your girlfriend, wife, female prostitute lover, or mistress if she accepts it and thinks it's a cute way of showing affection.
Origin:
Replace "teddy" in the word "teddy bear" with "titty"(meaning a woman's breast) and you get "titty bear!"
Ex1. So Titty Bear, shall we make love tonight?
Ex2: Little boys sleep with teddy bears, but big boys sleep with TITTY bears!
2.
a bear with tits...
"dude, look at the bear on those tits"