I recommend my patients to wear binders for the first two weeks after surgery (binders can be worn over the garment), and compression garment for 6 weeks. Consult your surgeon regarding post op care since each surgeon has a slightly different protocol.
There are a number of different ways to recover after BBL. A compression garment is needed where any liposuction was done, and I also have my patients limit their sitting for the first 2 weeks. There is not an accepted answer as to what type of compression is better. Foam, which can be cut to size and worn under a binder or garment to provide compression on certain areas, is often useful. Some surgeons will use a body suit type garment that does not place compression on the buttocks, with the thought fat survival may be improved. Best to listen to the specific recommendations of your doctor. When choosing a doctor, look for American Board of Plastic Surgery certification.