It emits light in all directions, but more if the filament is broadside rather than end on. You will probably not be able to sneak up to the radar sensor from any direction without triggering it, but it will be much more sensitive 'full frontal' rather than edge on.
Putting a flat mirror behind the light bulb would throw all of the light forwards and to the sides, but if you want a longer tighter beam like a torch or headlight, you need to use a parabolic reflector dish to focus all emissions into a tight beam. Same applies to the radar signal.
A bulb may not be bright enough to show up the odd small birds, but if a flock flew past, or a big bird, they would be more noticable. Similarly with your birds, they need to be collectively big enough to reflect back sufficient motion detection (doppler shift) to trigger the sensor. Also, a single small bird flying just in front of the sensor will reflect back much more signal than a big bird far away.
If you want to restrict where the light shines, you can't do it by swivelling the light bulb, you need to erect some sort of blinker to shield things from the light. Similarly with the radar sensor, use metal to shield off unwanted line-of sight regions.
If you want to be really selective, you could converge 2 different wide-apart focused beams on to the same required small target area, 'AND' their 2 sensor triggers, so only the pinpointed target is likely to cause sufficient reflected signal at the same time to trigger both devices and cause an alert.
The ebay link is in this post...