Do not expect Dark Souls' traditional 'shield up, creep forward' approach to combat. This is much faster, much more fluid, high-risk, high-reward stuff. For starters, there are no shields to be raised at all, Bloodborne's combat instead focusing on defense by way of attack. Instead of blocking and parrying in the traditional way, a side firearm now acts as your 'shield', its fast, on-the-fly reaction-shots able to interrupt and stagger attacking enemies if thrown out quickly enough.
Beyond that, large, folding melee weapons have multiple modes of attack for different situations, and molotovs stand in for magic. It's all very different, but through abstracted function, very much the same. Just don't get carried away with your newfound aggressive capabilities. Because, well, we all know what happens then.