What is the significance of the recurring dancing bear?
I think it's not a bear, it's a tiger (Tora). And according to wiki his name is Tanker-kun. 

For now it's some kind of mascot (no further details), because Hamatora (ハマトラ) means "Beach Tiger". And Tanker-kun always use sailor suit, so for now we can assume he's mascot of Hamatora.