Flying into Class B airspace frequently when instructing, I've come to understand that a vector by the controller into the airspace (or a climb into it, as well) constitutes a clearance into the Bravo airspace. The specific verbiage "Cleared into Class B airspace" is usually issued when you are given instructions that may or may not take you into the airspace.

For example, transitioning through or near to Bravo airspace and/or told to "proceed on course," that would be a case where they would need to specifically clear you into the airspace (e.g., "Cleared into Class B airspace"). If you were given a vector or altitude to fly that does take you into it, IFR or VFR, that constitutes your clearance into the airspace. FAR 91.131(a)(1) states a pilot must have an ATC clearance, which is accomplished even by a vector/altitude assignment by the authorized facility.