A few suggestions:
1) The white thing on the left side is all slanty and wobbly and drape-y, and it's not doing anything to help your control of shapes on the bottle. Neither are the huge unaccounted for gaps in between your control surfaces. You need to tighten the space.
a) You could move everything closer to the bed, and drop the product closer to the ground. Reduces gaps and lets your left side reflector lie more vertically, since you can just start it at the top of your mattress area and drop straight down.
b) Alternatively, buy another crossbar and stands. That's what I would do. Then everything is easy, rectilinear, totally controllable.
2) If, due to #1, the left is now reflecting more than you want, simply replace the white with the gray bedsheet you already own to compensate for that.
3) Mount the backdrop on a piece of black foamcore (couple dollars) instead of that white paper, to cut on unwanted bounces and patterns.
4) Also black foamcore on the floor.
5) Also black foamcore simply laid across the two crossbars (or the crossbar and the mattress, depending on 1a vs 1b) kills any ceiling bounce.
6) Spray your hanging sheets with water beforehand and let sit to help kill wrinkles that might show up in the reflection.
7) Flagging the sides of the gap between the umbrella and the sheet might help with bouncing patterns. Again, a piece of black foamcore (cut in half) on either side and just laid against the gap would do it.