Remember, in a fluorescent tube it is the phosphors on the inner surface of the tube that are emitting the light. When you put even a good mirror surface on the outside of the tube you just reflect light back to the phosphor, not out the opposite side - the tube is virtually opaque, so light can't pass through it well at all.
The reflective surface needs to be on a surface away from the bulb, and that surface needs to be tilted so the light from the back side is reflected so it doesn't just bounce back at the tube. One way to do that is to use an inverted "W" shape reflective surface. The light then strikes one slanted surface, reflects to the other slanted surface and down into the tank. Here is a sketch of what I am referring to: (This isn't the only way to do this, but it is one easy way.)