Light aircraft instructor pilot reported an NMAC in SEA Approach airspace and during evasive maneuvering they climbed into Bravo airspace.

Narrative

I was the instructor in the right seat conducting an IPC with the pilot flying in the left seat; operating the aircraft and radios while under the hood. We had been on with Seattle Approach for flight following for a VFR practice approach to RNT; the RNAV-Z for runway 16. ATC informed us they could only authorize a practice approach if we could maintain VFR outside the Bravo and below 2000 feet; which we accepted and descended as directed. We continued setting up for the approach.As we approach the hold entry at LUTSY; approach told us to maintain 2000; we were cleared for the approach; to maintain VFR and frequency change was approved. At this point we were close enough to the hold that I instructed the pilot to continue and enter the hold and we would contact the tower as we got established. Upon contacting the Tower it was clear there had not been any coordination as they were unaware of our presence; adding to a short amount of confusion when they instructed us to go back to Approach. At this point the pilot had entered the hold; I informed them to continue the hold and the approach and given that we were still well clear of the Renton airspace we could break off early if necessary. As we completed the hold and turned inbound we started our descent to remain below the Bravo.At this time we both had a traffic alert in Foreflight for an aircraft at our 3 o'clock; same altitude and possibly descending. I saw the aircraft visually approaching quickly and instructed the pilot to climb immediately and he complied. I tracked the aircraft until I was sure we were clear at which point I looked back down at the chart and realized we had climbed in to the 2000 foot Bravo shelf. I instructed the pilot to turn left; descend and to remove the hood. Once clear of the airspace we contacted Renton Tower again and requested a VFR transition through their airspace to the south back to the home airport.The combination of surprise alert; visual confirmation of the approaching aircraft; and confusion regarding ATC handoff resulted in me losing awareness of the position of the Bravo relative to our approach path.