Can you use AirPlay (for the image) and a bluetooth speaker at the same time

I am using Airplay to connect my ipad to an overhead projector. When I turn on a bluetooth speaker to show a video the mirroring on the overhead goes away and I just get the sound from the bluetooth speaker. If I go back to mirroring my ipad, the sound goes away. I have also tried plugging the speaker directly into the ipad, the picture stays that way but no sound is coming from the speaker. Need both to work to use this in a classroom but so far no success.