A good reflector will direct more light towards your plant, making it more efficient and effective for growth, but there will still be spillover light. If you are concerned about the glow, you will need to set up some sort of screen around that area of the room, or some serious light-blocking shade on the window.

I used an inexpensive room divider lined on the inside with Foylon, a reflective fabric. Gets the light back onto the plants and out of your eyes.

Foylon or mylar is made of aluminum (on plastic). This reflects the harmful infra-red and causes the room to be hotter. Better is the "panda paper" which is all plastic, white on one side and black on the other side. The black blocks the light, the white reflects the light in a diffused way for better coverage. The infra-red and heat tends to go through the plastic.

Also get a better-designed horizontal reflector that covers the whole bulb.

I think a new reflector will prove to make a marginal difference to solve the problem, but a good idea nonetheless. You could use an indoor, covered greenhouse such as Hydro-Hut or you could build something similar using various enclosed items such as an armoire or portable, covered greenhouse. Friends of mine framed-off an area in their basement in which to keep their garden so as to contain the light and to control the other environmental factors. A word of warning: any time you start containing plants and lights in an enclosed area you will have to monitor and possibly dissipate heat and/or humidity. Good luck.