Instructor pilot; on an IFR flight plan; reported taking evasive action after receiving a late report of traffic from ATC.

Narrative

My student and I were flying below the Class Bravo area back from ZZZ1 to ZZZ. We were flying from waypoint ZZZZZ1 to ZZZZZ. As we approached the ZZZZZ waypoint; an aircraft was departing from ZZZ2; and turned towards us.They seemed to be based in a different area. I saw them on my ADS-B; and that's when we made the evasive action to descend; however; if we were to turn left; the restricted area is about 1.5 to 2 miles from us. We decided to pull the power and descend immediately. Aircraft Y did NOT seem to want to give way at all and continued to go towards us. Approach gave us a very late traffic warning when they were only 1/2 a mile away. I cannot confirm if Aircraft Y was on an IFR flight plan; but this was uncalled for.What should have happened was to be given a traffic alert from Approach earlier to both pilots to provide us with more time to descend and for Aircraft Y to turn left to a different heading. Class Bravo shelf was at 2500; and we were told to stay out of Class Bravo and maintain VFR. It was hazy out; even though the weather was reporting 10 miles of visibility.