Do I wear compression garment for hip fat transfer and BBL? Will it compromise my results?

Personally, I am not a big fan of compression garments at all.  Yes, they can prevent swelling and most patients feel "supported" while wearing them.  I do not believe they improve your final results, however.
Similarly, there is disagreeement regarding putting compression over the grafted areas.  Some surgeons believe this helps shape the area whereas others believe the pressure may negatively affect the "take" of the fat grafts.  Hence, garments are available with and without the buttocks cut out.
To sum it up, I would be comfortable recommending you wear just an abdominal garment, or nothing at all.
Hope that helps!

We provide a butt-out compression garment that should be worn for several weeks after the procedure. 

Surgeons have different protocols regarding compression after BBL, so I recommend you follow your surgeons recommendations.  I typically recommend my patients wear compression garments over the liposuction-treated areas, but only very light or no compression to the grafted areas on the buttocks.  Excess compression theoretically may decrease the graft success.  Most surgeons recommend not sitting on the buttocks after fat grafting for this same reason.