You sort of do, actually.
You have to ring the co-op bell (the one to get help, not the one to help others) in almost all areas in the game for a Bell Maiden to appear and open you up for invaders (in NG anyway, can't speak for NG+). Only the zones where a Bell Maiden is present from the start have old fashioned invasions and even those can be stopped by killing the Bell Maiden.
Since I solo and or do summons to help others, I've never been invaded once in BB and I'm pretty far in.
Today I invaded someone who was alone in the
graveyard area (cant remember the name)