The surest way to take care of a large bubble that has formed in an air mattress is to use a repair kit that contains a patch and air mattress repair glue. You can buy the repair kit from any store that sells air mattresses. The air mattress needs to be completely flat for you to fix the air bubbles. The patch should be big enough to cover the bulged area, but check before applying the glue. Once the patch is ready, press it into the bulge, making sure it's completely flat against the air mattress and no air bubbles are present. Allow the patch to dry completely before refilling the air mattress with air.
Depending on the size of the bubble or bulge, sometimes it can be popped without putting a hole in the mattress. Press firmly into the air bubble to pop it. If it doesn't pop right away, open the air vent to get some of the air out of the mattress. As the air is coming out, continue to press firmly into the bubble until it pops. Once all the air is out of the mattress, walk over it to ensure there are no other hidden air bubbles in the mattress. Fill the mattress with air, and close the air vent so none of the air escapes.
Air bubbles and bulges typically happen due to leaks within the mattress. If you notice many air bubbles at once or that they happen frequently, let all the air out of the mattress and inspect it for small holes where air can leak out without you noticing. Look over the entire mattress on both sides. Any holes should be repaired before refilling the mattress, or the air bubbles will continue to appear.
When filling an air mattress, avoid overfilling it with air as this could cause it to expand too much and tear. Any tears in the mattress will cause leaks and may not be repairable, depending on the severity of the tear. When using a repair kit with glue, follow the instructions that come with the kit to assure you use it properly.