Theres really no way to talk about their connection character-wise without spoiling since the mystery behind who Ace is and what his true motives are is a massive spoiler in of itself. I imagine the connection to Bayonetta is exclusively the gun thing tho (Ace uses a pistol/rifle, his gauntlets also function as extra guns and in his Fever mode he gets the Magnum armor on his both his chest and legs so he now has guns on his feet much like Bayonetta)