The base of this costume is a nude leotard. Choose one that matches your skin tone, but it doesn't have to be perfect. (Compare prices online)
This costume was inspired by a Hussein Chalayan creation, but can be recreated on a non-designer budget. The plastic bubbles can be quickly imitated using balloons, but it is likely that someone will mistake you as a bunch of white grapes. Instead, I suggest using fillable Christmas ornaments. These clear plastic balls snap together easily, and have a high gloss just like Lagy Gaga's bubbles.
I suggest that you use both the 60mm and the 100mm clear plastic ornaments so that you have a variation in bubble size just like Gaga. I've already found these sizes for you, so you can check online for the best price.
Stitch 1" tabs of ribbon onto various parts of the leotard. Snap the ornament balls shut over the tabs so that the ornament balls have a good hold on the ribbon and stay in place. Tying a knot at the end of each ribbon tab can help.