I also tested out the bubble depth of field and it seems to be working the way that I want now. For this shot I added several layers of camera lens blurring to both the background and the bubbles as well as an animated vignette, motion blur, film grain and blurring the edges of the frame. I really want to bring the audience away from the room and focus on the simplicity of the soap bubbles in this shot.
I did notice some white circles in some of the bubbles, though. When I did my first tests several weeks ago I thought it was from the lights, but I think it's the reflections of the other bubbles in the scene. I'm not sure if this is due to the amount of rays in the scene or other settings, but I'll have to investigate this further. This may also change when I move the camera around. Hopefully I can get rid of them, but even with them there I like how the bubbles are looking.