A319 Captain reported an NMAC during approach to a class D airport under a Bravo shelf requiring evasive action to avoid a possible collision.

Narrative

During descent to ZZZ we were in Class B airspace (ZZZ1) descending to 4000. The bottom shelf of class B was 3000. At the point of the RA we were leveled off at 4000. We had noticed a target at approximately 5 miles showing 500 ft below us while at 4000 ft. We had divided our attention between the Navigation Displays (NDs) monitoring the traffic as well as trying to make contact visually. The Air Traffic Controller had pointed the traffic out and we noticed the target continued to close in on us head on. Eventually we received a 'Traffic' TCAS call and watched as the target closed in on us. Additionally; the target began to climb and I saw the last altitude as 300 ft below us while we go the RA. The RA was a monitor vertical speed but the memory item was executed with Autopilot off and Flight Director (FD) off. The First Officer (FO) said that he still saw the target climbing into us and I called climb. We ascended to 4300 ft and the Clear Of Conflict announcement was given. During this time I was trying to contact the controller but I was saturated with other aircraft and not until the conflict was resolved did the controller actually come back to us and question if we had received an RA. The aircraft was returned back to 4000 ft and a normal landing was commenced. Is there a way to keep our aircraft in Class B airspace to quickly proceed to the ZZZ airport at a higher altitude. Even though this occurred within Class B airspace; being below class B would force even more threats like this from the surrounding GA training aircraft.