Please refer to my YouTube video on Mounting Works on paper onto panel.
A few things I thought about trying (but haven't yet) is spritzing the backside of a large acrylic painting to allow it to expand and lay more flat prior to mounting it on top of the adhesive which is only applied to the panel. If I did do that, you would like lose some of the perimeter of the painting, due to expansion of the painting. YOu would spritz the backside first with water, and then allow it to sit there for about 5 minutes, then remove all of the water with a dry towel so it is just damp. Then, when you lay the acrylic painting bottom side against the adhesive, it should lay much flatter. For any work larger than 30x30in, I would recommend a second set of hands to help you lay the painting down!
If your painting is cwm/oil on paper, sprtizing with water would be an "experiment" - I wouldn't try this for a show ready piece - but perhaps an experimental piece - because while Gamblin Colors said it is "probably okay" I have not tried it and am not sure it would work - but I do think it might help prevent any bubbles.
If you get bubbles here and there for either type of work, do not worry. Once everything is dry, you can take a very sharp (new) razor blade, slit through the bubble, add adhesive inside the area, and then smooth it out. You really can't see hits surgical procedure when it is all gued down but if you do see some hit of the slit, just cover over with a bit of paint! This one technique takes away the fear of the whole process!
Definitely use a brayer and cotton cloth over the painting after mounting it; work from the center outword so bubbles get pushed to the outside edges of the painting. Be methodical and systematic - don't brayer haphazardly - the point is to move all bubbles out from the inside out!