The way most drivers end up with that is by installing tires that are just a few centimeters too wide for their rims. The idea is to increase the size of the contact patch but in alot of cases the sidewall just ends up flexing during lateral movement and your contact patch suffers. While it might be a good idea on drag strip funny cars it doesn't do a whole lot of good for daily drivers.
That being said the stock rubber on 08+ wrx is 235/45/17, many drivers will choose to go with a wider tire like a 245/40/17 while the contact patch is 1cm wider the sidewall is .5cm shorter (on both sides). this allows the driver to increase their contact patch by 2-4% without much negative effect on the contact patch.
If your interested in the bulging for the look then you may look for tires with particularly soft sidewalls, they will bulge under the weight of the car and the tire pressure but they arent so good for daily driving as they perform poorly when turning in particular.
13 WRX Hatch - Torqued Performance Stage 1+
Slow is Smooth > Smooth is Fast