In the second light novel there was a device called "the beast's head" that allowed Dante to traverse to other dinensions/timelines.
So using that as a way of connecting the two franchises, as they could be set on the same world but branching timelines.
If that's too much work, then just doing a trip thru the multiverse would be cool.
EDIT- I never read the novel so I don't know how the device actually works. Plus people have pointed out Bayonetta is more outlandish and cartoony than DMC.
But DMC was never really known consistentency now was it